CHAPTER 2 Motion Your one-stop online resource connectED.mcgraw-hill.com ? Video WebQuest Audio Assessment Review Concepts in Motion g Inquiry Multilingual eGlossary Launch Lab Animal Race A cheetah can run at a speed of almost 120 km/h. It is the fastest runner in the world. A horse can reach a speed of 64 km/h, an elephant’s top speed is about 40 km/h, and a tortoise walks at a speed of about 0.3 km/h. The speed of an object is calculated by dividing the distance that the object travels by the time it takes it to move that distance. How does your speed compare to the speeds of these animals? For a lab worksheet, use your StudentWorks™ Plus Online. ? Inquiry Launch Lab Make a three-tab book. Label it as shown. Use it to organize your notes on motion. Displacement Velocity Acceleration Motion 0042_0043_C02CO_894583.indd 42 5/3/10 12:15 PM THEME FOCUS Motion and Forces Section 1 • Describing Motion Objects are in motion all around us. Section 2 • Velocity and BIG Idea Motion occurs when an object changes its position. Momentum Section 3 • Acceleration Chapter 2 • Motion 0042_0043_C02CO_894583.indd 43 43 5/3/10 12:16 PM SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. ALSO COVERS MA.912.S.1.2 Section 1 Reading Preview Describing Motion Essential Questions MAIN Idea Position describes where an object is, and speed ◗ How are distance and describes how fast the object is moving. displacement different? ◗ How is an object’s speed calculated? ◗ What information does a distance-time graph provide? Real-World Reading Link How would you describe the trip from your home to your school? You might include whether you walked or rode a bus, how far away the school was, and how long it took to get there. Scientists describe motion in a similar, but very specific way. Review Vocabulary Motion and Position meter: the SI unit of length, abbreviated m You do not always need to see something move to know that motion has taken place. For example, suppose you look out a window and see a mail truck stopped next to a mailbox, as shown in Figure 1. One minute later, you look out again and see the same truck stopped farther down the street. Although you did not see the truck move, you know it moved because its position relative to the mailbox changed. New Vocabulary motion displacement speed g Multilingual eGlossary ■ Figure 1 As the mail truck follows its route, it stops at each mailbox along the street. Explain How do you know the mail truck has moved? 9:00 A.M. 44 Reference points A reference point is needed to determine the position of an object. In Figure 1, the reference point might be a mailbox. Motion is a change in an object’s position relative to a reference point. How you describe an object’s motion depends on the reference point that is chosen. For example, the description of the mail truck’s motion in Figure 1 would be different if the reference point were a tree instead of a mailbox. After a reference point is chosen, a frame of reference can be created. A frame of reference is a coordinate system in which the position of the object is measured. The x-axis and y-axis of the reference frame are drawn so that they are perpendicular to each other and intersect the reference point. 9:01 A.M. Chapter 2 • Motion 0044_0050_C02S1_894583.indd 44 5/7/10 9:42 AM Coordinate systems Figure 2 shows a map of the city where the mail truck is delivering mail with a coordinate system drawn on it. The x-axis is in the east-west direction, the y-axis is in the north-south direction, and each division represents a city block. The post office is located at the origin. The mail truck is located at 3 blocks east (x = 3) and 2 blocks north (y = 2) of the post office. 2 Change in Position -2 Have you ever run a 50-m dash? Describing how far and in what direction you moved was an important part of describing your motion. -3 4 N 0m 10 m 20 m 40 m Post ofﬁce 0 -1 -4 -4 -3 -2 -1 0 1 2 3 4 ■ Figure 2 A coordinate system is like a map. The reference point is at the origin, and each object’s position can be described with its coordinates. Identify the position of the orange car. VOCABULARY SCIENCE USAGE V. COMMON USAGE Position Science usage the location of an object in relation to a reference point The cat’s position was 3 meters west of the house. Common usage a point of view; a job or rank After graduation, I accepted a teller position at the bank. 50 m 30 m S TA R T FINISH 20 m 30 m N 1 Distance In a 50-m dash, each runner travels a total distance of 50 m. The SI unit of distance is the meter (m). Longer distances are measured in kilometers (km). One kilometer is equal to 1,000 m. Shorter distances are measured in centimeters (cm) or millimeters (mm). One meter is equal to 100 cm and to 1,000 mm. Displacement Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark, as shown in Figure 3. The runner travels 50 m in the original direction (east) plus 30 m in the opposite direction (west), so the total distance that she ran is 80 m. How far is she from the starting line? The answer is 20 m. Sometimes, you may want to know the change in an object’s position relative to the starting point. An object’s displacement is the distance and direction of the object’s change in position. In Figure 3, the runner’s displacement is 20 m east. The length of the runner’s displacement and the total distance traveled would be the same if the runner’s motion were in a single direction. For example, if the runner ran east from the starting line to the finish line without changing direction, then the distance traveled would be 50 m and the displacement would be 50 m east. Mail truck 3 50 m ■ Figure 3 An object’s displacement is not the same as the total distance that the object traveled. The runner’s displacement is 20 m east of the starting line. However, the total distance the runner traveled is 80 m. Describe the difference between the total distance traveled and the displacement. Section 1 • Describing Motion 0044_0050_C02S1_894583.indd 45 45 5/13/10 9:45 AM 5m east 5m east 10 m east Displacements in the same direction can be added. ■ Figure 4 These arrows represent the students’ walks. The green arrows show the first part of the walk and the purple arrows show the second part. The red arrows show the students’ displacements. FOLDABLES Incorporate information from this section into your Foldable. 5m east st ea 10 m east h ort 5 m west Displacements in opposite directions can be subtracted. n 5m 4 m east 3 m north Displacements that are not in the same direction or opposite directions cannot be directly added or subtracted. Adding displacements You know that you can add distances together to get the total distance. For example, 2 m + 3 m = 5 m. But how would you add the displacements 5 m east and 10 m east? Directions in math problems are much like units: you can add numbers with like directions. For example, suppose a student walks 5 m east, stops at a crosswalk, and then walks another 5 m east, as shown on the left in Figure 4. His displacement is 5 m east + 5 m east = 10 m east But what if the directions are not the same? Then compare the two directions. If the directions are exactly opposite, the distances can be subtracted. Suppose a student walks 10 m east, turns around, and walks 5 m west, as shown in the center of Figure 4. The size of the displacement would be 10 m − 5 m = 5 m Rules for Table 1 Adding Displacements The direction of the total displacement is always the direction of the larger displacement. In this case, the larger displacement is east, so the total displacement is 5 m east. Now suppose the two displacements are not in the same direction or in opposite directions, as illustrated on the right in Figure 4. Here, the student walks 4 m east and then 3 m north. The student walks a total distance of 7 m, but the displacement is 5 m in a roughly northeast direction. 4 m east and 3 m north cannot be directly added or subtracted, and they should be discussed separately. The rules for adding displacements are summarized in Table 1. 1. Add displacements in the same Speed direction. 2. Subtract displacements in opposite directions. 3. Displacements that are not in the same or in opposite directions cannot be directly added together. 46 Think back to the mail truck moving down the street. You could describe the movement by the distance traveled or by the displacement. You might also want to describe how fast the truck is moving. To do this, you need to know how far it travels in a given amount of time. To describe how fast an object moves, scientist use the object’s speed. Speed is the distance an object travels per unit of time. Chapter 2 • Motion 0044_0050_C02S1_894583.indd 46 5/7/10 9:43 AM Calculating speed Any change over time is called a rate. For example, you could describe how quickly water is leaking from a tank by stating how many liters are lost each hour. This would be the rate of water leakage. If you think of distance as the change in position, then speed is the rate of change in position. Speed can be calculated from this equation. Speed Equation distance (in meters) time (in seconds) speed (in meters/second) = __ d s=_ t Table 2 Common Speeds Motion Speed (m/s) Olympic 100-m dash 10 m/s Car on city street (35 mph) 16 m/s Car on interstate highway (65 mph) 30 m/s Commercial airplane 250 m/s In SI units, distance is measured in meters and time is measured in seconds. Therefore, the SI unit for speed is meters per second (m/s). Sometimes, it is more convenient to express speed in other units, such as kilometers per hour (km/h). Table 2 shows the speeds of some common objects. ? Inquiry Virtual Lab SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. EXAMPLE Problem 1 Calculate Speed A car traveling at a constant speed covers a distance of 750 m in 25 s. What is the car’s speed? Identify the Unknown: speed: s List the Knowns: distance: d = 750 m time: t = 25 s Set Up the Problem: Solve the Problem: Check the Answer: PRACTICE Problems 750 m s = _td= _ 25 s 750 m _ s= = 30 m/s 25 s 30 m/s is approximately the speed limit on a U.S. interstate highway, so the answer is reasonable. Find Additional Practice Problems in the back of your book. 1. A passenger elevator travels from the first floor to the 60th floor, a distance of 210 m, in 35 s. What is the elevator’s speed? Review Additional Practice Problems 2. A motorcycle is moving at a constant speed of 40 km/h. How long does it take the motorcycle to travel a distance of 10 km? 3. How far does a car travel in 0.75 h if it is moving at a constant speed of 88 km/h? 4. Challenge A long-distance runner is running at a constant speed of 5 m/s. How long does it take the runner to travel 1 km? Section 1 • Describing Motion 0044_0050_C02S1_894583.indd 47 47 5/7/10 9:43 AM ■ Figure 5 The cyclist’s speed varies from 0 km/h to 30 km/h during his trip. Speed Changing over Distance Explain how you can describe the Speed (km/h) speed of an object when the speed is changing. 30 Going downhill 25 Climbing steep hill Stopping for red light 20 15 Constant speed 10 5 0 Gaining speed 1 2 3 4 5 Distance (km) SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. ? Inquiry MiniLab Measure Average Speed Procedure 1. Read the procedure and safety 2. 3. 4. 5. information, and complete the lab form. Mark a point on the floor with tape. Place a toy car at this point. Give the toy car a gentle push forward. At the same time, start a stopwatch. Record the time it takes for the car to come to a stop. Use a meterstick to measure the distance the car traveled. Analysis 1. Calculate the average speed of the car in m/s. 2. Infer How would the average speed change if you gave the car a harder push? Try it. 48 Constant speed Suppose you are in a car traveling on a nearly empty freeway. You look at the speedometer and see that the car’s speed hardly changes. If the car neither slows down nor speeds up, the car is traveling at a constant speed. If you are traveling at a constant speed, you can calculate your speed by dividing any distance interval over the time it took you to travel that distance. The speed you calculate will be the same regardless of the interval you choose. Changing speed Usually, speed is not constant. Think about riding a bicycle for a distance of 5 km. The bicycle’s speed will vary, as in Figure 5. As you start out, your speed increases from 0 km/h to 20 km/h. You slow down to 10 km/h as you pedal up a steep hill and speed up to 30 km/h going down the other side of the hill. You stop for a red light, speed up again, and move at a constant speed for a while. Finally, you slow down and come to a stop. Checking your watch, you find that the trip took 15 min. How would you express your speed on such a trip? Would you use your fastest speed, your slowest speed, or some speed between the two? Two common ways of expressing a changing speed are average speed and instantaneous speed. Average speed Average speed is one way to describe the speed of the bicycle trip. Average speed is the total distance traveled divided by the total time of travel. It can be calculated using the relationships between speed, distance, and time. For the bicycle trip just described, the total distance traveled was 5 km and the 1 h, or 0.25 h. Therefore, the average speed was total time was _ 4 d 5 km =_ = 20 km/h s=_ t 0.25 h Chapter 2 • Motion 0044_0050_C02S1_894583.indd 48 5/7/10 9:43 AM Instantaneous speed Suppose you watch a car’s speedometer, like the one in Figure 6, go from 0 km/h to 80 km/h. A speedometer shows how fast a car is going at one point in time, or at one instant. The speed shown on a speedometer is the instantaneous speed. Instantaneous speed is the speed at a given point in time. When something is speeding up or slowing down, its instantaneous speed is changing. The speed is different at every point in time. If an object is moving with constant speed, the instantaneous speed does not change. The speed is the same at every point in time. Reading Check Identify two examples of motion in which an object’s ■ Figure 6 A speedometer gives the car’s instantaneous speed. Instantaneous speed is the speed at one instant in time. instantaneous speed changes. Graphing Motion The motion of an object over a period of time can be shown on a distance-time graph. For example, the graph in Figure 7 shows the distance traveled by three swimmers during a 30-minute workout. Time is plotted along the horizontal axis of the graph, and the distance traveled is plotted along the vertical axis of the graph. Each axis must have a scale that covers the range of numbers to be plotted. In Figure 7, the distance scale must range from 0 to 2,400 m and the time scale must range from 0 to 30 min. Next, the x-axis is divided into equal time intervals, and the y-axis is divided into equal distance intervals. Once the scales for each axis are in place, the data points can be plotted. In Figure 7, there is a data point plotted for each swimmer every two and a half minutes. After plotting the data points, a line is drawn connecting the points. Distance-Time Graph Mary 2,400 2,200 Distance (m) 2,000 Kathy 1,800 1,600 Animation 1,400 Julie 1,200 1,000 800 600 400 200 0 Concepts in Motion 0 10 20 Time (min) 30 ■ Figure 7 This graph shows how far each girl swam during a 30 minute workout. Time is divided into 2.5-minute intervals along the x-axis. Distance swam is divided into 200-m intervals along the y-axis. Examine the graph and determine which girl swam the farthest during the workout. Section 1 • Describing Motion 0044_0050_C02S1_894583.indd 49 49 5/7/10 9:43 AM Distance-Time Graph Mary 2,400 2,200 Distance (m) 2,000 Kathy 1,800 v = 80 m/min 1,600 1,400 v = 60 m/min 1,200 Julie 1,000 800 v = 0 m/min 600 v = 80 m/min 400 200 0 0 v = 40 m/min 10 20 30 Time (min) ■ Figure 8 An object’s speed is equal to the slope of the line on a distance-time graph. Identify the part of the graph that shows one of the swimmers resting for 10 min. Section 1 Review Section Summary ◗ Motion occurs when an object changes its position relative to a reference point. ◗ Displacement is the distance and direction of a change in position from the starting point. ◗ Speed is the rate at which an object’s position changes. ◗ On a distance-time graph, time is the Speed on distance-time graphs If an object moves with constant speed, the increase in distance over equal time intervals is the same. As a result, the line representing the object’s motion is a straight line. For example, look at the graph of the swimmers’ workouts in Figure 8. The straight red line represents the motion of Mary, who swam with a constant speed of 80 m/min. The green line represents the motion of Julie, who did not swim with a constant speed. She swam with a constant speed of 40 m/min for 10 minutes, rested for 10 minutes, and then swam with a constant speed of 80 m/min for 10 minutes. The graph shows that the line representing the motion of the faster swimmer is steeper. The steepness of a line on a graph is the line’s slope. The slope of a line on a distance-time graph equals the object’s speed. Because Mary has a greater speed (80 m/min) than Kathy (60 m/min), the line representing her motion has a larger slope. Now look at the green line representing Julie’s motion. During the time she is resting, her line is horizontal. A horizontal line on a distance-time graph has zero slope and represents an object at rest. SC.912.P.12.2, MA.912.S.1.2 5. MAIN Idea Describe the trip from your home to school using the words position, distance, displacement, and speed. 6. Explain whether the size of an object’s displacement could be greater than the distance the object travels. 7. Describe the motion represented by a horizontal line on a distancetime graph. 8. Describe the difference between average speed and constant speed. 9. Think Critically During a trip, can a car’s instantaneous speed ever be greater than its average speed? Explain. x-axis and distance is the y-axis. ◗ The slope of a line plotted on a distance- time graph is the speed. Apply Math 10. Calculate Speed Michiko walked a distance of 1.60 km in 30 min. Find her average speed in m/s. 11. Calculate Distance A car travels at a constant speed of 30.0 m/s for 0.80 h. Find the total distance traveled in km. 50 Chapter 2 • Motion 0044_0050_C02S1_894583.indd 50 Assessment Online Quiz 5/7/10 9:43 AM SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. ALSO COVERS: MA.912.S.1.2 Section 2 Reading Preview Velocity and Momentum Essential Questions MAIN Idea An object’s velocity describes the object’s speed and ◗ What is the difference between direction of motion. speed and velocity? ◗ How is the motion of two objects relative to each other described? ◗ How can an object’s momentum be calculated? Real-World Reading Link Cars, trucks, and many other vehicles can go both backward and forward. The driver must put the car in the proper gear for each direction. What could happen if the driver put the car into reverse instead of forward? Review Vocabulary Velocity speed: rate of change of position You turn on the radio and hear a news story about a hurricane. The storm, traveling at a speed of 20 km/h, is located 500 km east of your location. Should you worry? Unfortunately, you do not have enough information to answer that question. Knowing only the speed of the storm is not much help. Speed describes only how fast something is moving. To decide whether you need to move to a safer area, you also need to know the direction that the storm is moving. In other words, you need to know the velocity of the storm. Velocity includes the speed of an object and the direction of its motion. Velocity has the same units as speed, m/s. If you had been told that the hurricane was traveling straight toward your house at 20 km/h, you would have known to evacuate. New Vocabulary velocity momentum g Multilingual eGlossary FOLDABLES Incorporate information from this section into your Foldable. Velocity and speed Because velocity depends on direction as well as speed, the velocity of an object can change even if the speed of the object remains constant. For example, the race cars in Figure 9 have constant speeds through the turn. Even though the speeds remain constant, their velocities changes because they change direction thoughout the turn. Reading Check Describe how velocity and speed are different. Figure 9 These cars travel at constant speed, but not with constant velocity. The cars’ velocities change because their direction of motion changes. ■ Section 2 • Velocity and Momentum 0051_0055_C02S2_894583.indd 51 51 5/3/10 12:20 PM Same speed, different velocities It is possible for two objects to have the same speed but different velocities. For example, the two escalators pictured in Figure 10 are moving at the same speed but in opposite directions. The speeds of the two sets of passengers are the same, but their velocities are different because they are moving in different directions. Cars traveling in opposite directions on a road with the same speed also have different velocities. Motion of Earth’s Crust ■ Figure 10 The two escalators move with a speed of 0.5 m/s. But the left escalator’s velocity is 0.5 m/s downward and the right escalator’s velocity is 0.5 m/s upward. VOCABULARY WORD ORIGIN Velocity from the Latin veloci– meaning fast, swift, or rapid. The students found that the velociraptor’s velocity was 10 m/s north. Concepts in Motion Animation ■ Figure 11 Geologic evidence suggests that Earth’s surface is changing. The continents have moved slowly over time and are still moving today. Can you think of something that is moving so slowly that you cannot detect its motion, but you can see evidence of its motion over long periods of time? As you look around the surface of Earth from year to year, its basic structure seems the same. Mountains, plains, and oceans seem to remain unchanged. Yet, if you examined geologic evidence of what Earth’s surface looked like over the past 250 million years, you would see that large changes have occurred. Figure 11 shows how, according to the theory of plate tectonics, the positions of landmasses have changed during this time. Changes in the landscape occur constantly as continents drift slowly over Earth’s surface. These moving plates cause geologic changes, such as the formation of mountain ranges, earthquakes, and volcanic eruptions. The movement of the plates changes the size of the oceans. The Pacific Ocean is getting smaller, and the Atlantic Ocean is getting larger. The plates’ movement also changes the shape of the continents as they collide and spread apart. Plates move so slowly that their speeds are given in units of centimeters per year. Along the San Andreas Fault in California, two plates move past each other with an average speed of about 1 cm per year. The Australian Plate moves faster and pushes Australia north at an average speed of about 17 cm/y. Therefore, the velocity of the Austrailian plate is 17 cm/y north. About 250 million years ago, the continents formed a supercontinent called Pangaea. 52 Pangaea separated into smaller pieces. About 66 million years ago, the continents looked like the ﬁgure above. Chapter 2 • Motion 0051_0055_C02S2_894583.indd 52 5/3/10 12:21 PM 60 km 70 km 20 km/h 20 km/h 10 km/h 10 km/h 10 km 20 km 60 km West 40 km 30 km 20 km 10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km 30 km 20 km 10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km West East East 2:00 P.M. 3:00 P.M. ■ Relative Motion Have you ever watched cars pass you on the highway? Cars traveling in the same direction often seem to creep by, while cars traveling in the opposite direction seem to zip by. This apparent difference in speeds is because the reference point— your vehicle—is also moving. The choice of a moving reference point affects how you describe motion. For example, the motion of a hurricane can be described using a stationary reference point, such as a house. Figure 12 shows the locations and velocities of a hurricane and a car relative to a house at 2:00 p.m. and 3:00 p.m. The distance between the hurricane and the house is decreasing at a rate of 20 km/h. The distance between the house and the car is increasing at a rate of 10 km/h. How would the description of the hurricane’s motion be different if the reference point were a car traveling at 10 km/h west? Figure 13 shows the motion of the hurricane and the house relative to the car. A person in the car would say that the hurricane is approaching with a speed of 10 km/h and that the house is moving away at a speed of 10 km/h. It is important to notice that Figure 12 and Figure 13 show the same changes, but they use different reference points. Velocity and position always depend on the point of reference chosen. Figure 12 If the house is chosen for the reference point, the car appears to be traveling 10 km/h west and the hurricane appears to be traveling 20 km/h west. ■ Figure 13 If the car is chosen as the reference point, the hurricane appears to be moving towards the car at 10 km/h and the house is moving away from the car at 10 km/h. 60 km 70 km 10 km/h 10 km/h 10 km/h 10 km 10 km/h 20 km 60 km West West East 2:00 P.M. 40 km 10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km 70 km 80 km 10 km 0 km 10 km 20 km 30 km 40 km 50 km 60 km 70 km 80 km East 3:00 P.M. Section 2 • Velocity and Momentum 0051_0055_C02S2_894583.indd 53 53 5/3/10 12:21 PM Typical Table 3 Momentums Momentum (kg·m/s) Object Tossed baseball 0.15 Person walking 100 Car on interstate ? Inquiry 45,000 Momentum An object is moving at 2 m/s toward a glass vase. Will the vase be damaged in the collision? If the object has a small mass, like a bug, a collision will not damage the vase. But if the object has a larger mass, like a car, a collision will damage the vase. A useful way of describing both the velocity and mass of an object is to state its momentum. The momentum of an object is the product of its mass and velocity. Momentum is usually represented by the symbol p. Momentum Equation Video Lab momentum (in kg·m/s) = mass (in kg) × velocity (in m/s) What’s PHYSICAL and EARTH SCIENCE Got To Do With It? p = mv Video EXAMPLE Problem 2 The unit for momentum is kg·m/s. Like velocity, momentum has a size and a direction. An object’s momentum is always in the same as the direction as its velocity. Table 3 shows the sizes of the momentums of some common objects. SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. Solve for Momentum At the end of a race, a sprinter with a mass of 80.0 kg has a velocity of 10.0 m/s east. What is the sprinter’s momentum? Identify the Unknown: momentum: p List the Knowns: mass: m = 80.0 kg velocity: v = 10.0 m/s east Set Up the Problem: p = mv = (80.0 kg) × (10.0 m/s) east Solve the Problem: p = (80.0 kg)(10.0 m/s) east = 800.0 kg·m/s east Check the Answer: Our answer makes sense because it is greater than the momentum of a walking person, but much smaller than the momentum of a car on the highway. PRACTICE Problems Find Additional Practice Problems in the back of your book. 12. What is the momentum of a car with a mass of 1,300 kg traveling north at a speed of 28 m/s? Review Additional Practice Problems 13. A baseball has a momentum of 6.0 kg·m/s south and a mass of 0.15 kg. What is the baseball’s velocity? 14. Find the mass of a person walking west at a speed of 0.8 m/s with a momentum of 52.0 kg·m/s west. 15. Challenge The mass of a basketball is three times greater than the mass of a softball. Compare the momentums of a softball and a basketball if they both are moving at the same velocity. 54 Chapter 2 • Motion 0051_0055_C02S2_894583.indd 54 5/3/10 12:21 PM 30 m/s 30 m/s 900,000 kg·m/s 45,000 kg·m/s 30,000 kg 1,500 kg ■ Figure 14 Both the car and the truck have a velocity of 30 m/s west, but the truck has a much larger momentum. Comparing momentums Think about the car and the truck in Figure 14. Which has the larger momentum? The truck does because it has more mass. When two objects travel at the same velocity, the object with more mass has a greater momentum. A difference in momentums is why a car traveling at 2 m/s might damage a porcelain vase, but an insect flying at 2 m/s will not. Now consider two 1-mg insects. One insect flies at a speed of 2 m/s, and the other flies at a speed of 4 m/s. The second insect has a greater momentum. If two objects have the same mass, the object with the larger velocity has the larger momentum. Section 2 Review Section Summary ◗ The velocity of an object includes the object’s speed and its direction of motion relative to a reference point. ◗ An object’s motion is always described rel- ative to a reference point. ◗ The momentum of an object is the product of its mass and velocity: p = mv. SC.912.P.12.2, MA.912.S.1.2 16. Describe a car’s velocity as it goes around a track at a constant speed. MAIN Idea 17. Explain why streets and highways have speed limits rather than velocity limits. 18. Identify For each of the following news stories, determine whether the object’s speed or velocity is given: the world record for the hundred-meter dash is about 10 m/s; the wind today is 30 km/h from the north-west; a 200,000 kg train was traveling north at 70 km/h when it derailed; a car was issued a ticket for traveling at 140 km/h on the interstate. 19. Think Critically You are walking toward the back of a bus that is moving forward with a constant velocity. Describe your motion relative to the bus and relative to a point on the ground. Apply Math 20. Calculate Momentum What is the momentum of a 100-kg football player running north at a speed of 4 m/s? 21. Compare the momentums of a 6,300-kg elephant walking 0.11 m/s and a 50-kg dolphin swimming 10.4 m/s. Assessment 0051_0055_C02S2_894583.indd 55 Online Quiz Section 2 • Velocity and Momentum 55 5/3/10 12:21 PM SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. ALSO COVERS: SC.912.N.4.1, MA.912.S.1.2, MA.912.S.3.2 Section 3 Reading Preview Acceleration Essential Questions MAIN Idea Acceleration describes how the velocity of an object ◗ How are acceleration, time, and velocity related? ◗ What are three ways an object can accelerate? ◗ How can an object’s acceleration be calculated? ◗ What are the similarities and differences between straight line motion, circular motion, and projectile motion? Review Vocabulary velocity: describes the speed and direction of a moving object New Vocabulary acceleration centripetal acceleration g Multilingual eGlossary Video BrainPOP is changing with time. Real-World Reading Link If you have ever ridden on an airplane, you know that the plane taxis at a slow speed. Once on the runway, you are pressed back against your seat as the plane speeds up until it is going fast enough to take off. When the plane speeds up, it is accelerating. Velocity and Acceleration You are sitting in a car at a stoplight when the light turns green. The driver steps on the gas pedal and the car starts moving faster and faster. Just as speed is the rate of change of position, acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. Remember that velocity includes the speed and direction of an object. Therefore, a change in velocity can be either a change in speed or a change in direction. Acceleration occurs when an object changes its speed, its direction, or both. When you think of acceleration, you probably think of something speeding up. However, an object that is slowing down also is accelerating, as is an object that is changing direction. Figure 15 shows the three ways an object can accelerate. Reading Check Identify three ways that an object can accelerate. Figure 15 An object, such as this car, is accelerating if it is speeding up, slowing down, or changing direction. ■ Acceleration Like velocity and momentum, acceleration has a direction. If you look at the car in Figure 15, you will see that when it is speeding up, its acceleration and velocity are in the same direction. When the car is slowing down, its acceleration is in the opposite direction of its velocity. When the car changes direction, the acceleration is not in the same direction or opposite direction as the car’s velocity. Acceleration Velocity Velocity Velocity Acceleration Speeding Up 56 Slowing Down Changing Direction Chapter 2 • Motion 0056_0060_C02S3_894583.indd 56 5/7/10 10:06 AM ■ Figure 16 For objects that are speeding up and slowing down, the slope of the line on a speed-time graph is the acceleration. Speed of Tamara’s Car Moving at a constant speed Speed (km/h) 25 20 Slowing down at a red light 10 0 1 Parking Stopped at red light Pulling out of driveway 5 0 Slowing down to enter parking lot Speeding up 15 Identify the time intervals when Tamara’s car is not accelerating. 2 3 4 5 6 7 Time (min) Speed-time graphs and acceleration When an object travels in a straight line and does not change direction, a graph of speed versus time can provide information about an object’s acceleration. Figure 16 shows the speed-time graph of Tamara’s car as she drives to the store. Just as the slope of a line on a distance-time graph is the object’s speed, the slope of a line on a speed-time graph is the object’s acceleration. For example, when Tamara pulls out of her driveway, the car’s acceleration is 0.33 km/min2, which is equal to the slope of the line from t = 0 to t = 0.5 min. Calculating acceleration Acceleration is the rate of change in velocity. To calculate the acceleration of an object, the change in velocity is divided by the length of the time interval over which the change occurred. The change in velocity is final velocity minus the initial velocity. If the direction of motion does not change and the object moves in a straight line, the size of the change in velocity can be calculated from the change in speed. Then, the acceleration of an object can be calculated from the following equation. SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. ? Procedure 1. Read the procedure and safety 2. 3. 4. 5. acceleration change in velocity (in meters/second) time (in seconds) vf - vi _ a= t = ____ In SI units, velocity has units of m/s and time has units of s, so the SI unit of acceleration is m/s2. In some cases, your calculations will result in a negative acceleration. The negative sign means in the opposite direction. For example, an acceleration of −10 m/s2 north is the same as 10 m/s2 south. MiniLab Determine the Direction of Acceleration Acceleration Equation (in meters/second2) Inquiry information, and complete the lab form. Tape a bubble level onto the top of a laboratory cart and center the bubble. Tie a string to the front of the cart. Pull the cart forward, and observe the direction of the motion of the bubble. Move the cart at a constant speed, and observe the direction of the motion of the bubble. Allow the cart to coast to a stop, and observe the direction of the motion of the bubble. Analysis 1. Relate the motion of the bubble to the acceleration of the cart. 2. Predict how the bubble would move if you tie the string to the back of the cart and repeat the experiment in the opposite direction. Try it. Section 3 • Acceleration 0056_0060_C02S3_894583.indd 57 57 5/7/10 10:06 AM SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. EXAMPLE Problem 3 Calculate Acceleration A skateboarder has an initial velocity of 3 m/s west and comes to a stop in 2 s. What is the skateboarder’s acceleration? Identify the Unknown: acceleration: a List the Knowns: initial velocity: v i = 3 m/s west final velocity: v f = 0 m/s west time: t = 2 s (v - v ) Set Up the Problem: (0 m/s - 3 m/s) f i a=_ = __ west t Solve the Problem: (0 m/s - 3 m/s) a = __ = -1.5 m/s2 west 2s 2s The acceleration has a negative sign, so the direction is reversed. a = 1.5 m/s2 east Check the Answer: PRACTICE Problems The magnitude of the acceleration (1.5 m/s2) is reasonable for a skateboard that takes 2 s to slow from 3 m/s to 0 m/s. The acceleration is in the opposite direction of the velocity, so the skateboard is slowing down, as we expected. Find Additional Practice Problems in the back of your book. 22. An airplane starts at rest and accelerates down the runway for 20 s. At the end of the runway, its velocity is 80 m/s north. What is its acceleration? Review Additional Practice Problems 23. A cyclist starts at rest and accelerates at 0.5 m/s2 south for 20 s. What is the cyclist’s final velocity? 24. Challenge A ball is dropped and falls with an acceleration of 9.8 m/s2 downward. It hits the ground with a velocity of 49 m/s downward. How long did it take the ball to fall to the ground? Motion in Two Dimensions So far, we have only discussed motion in a straight line. But most objects are not restricted to moving in a straight line. Recall that we cannot add measurements that are not in the same or opposite directions. So, we will discuss motion in each direction separately. For example, suppose a student walked three blocks north and four blocks east. The trip could be described this way: the student walked north for three blocks at 1 m/s and then walked east for four blocks east at 2 m/s. Recall that objects that change direction are accelerating. For an object that is changing direction, its acceleration is not in the same or opposite direction as its velocity. This means that we cannot use the acceleration equation. Just as with displacement and velocity, accelerations that are not in the same or opposite directions cannot be directly combined. 58 Chapter 2 • Motion 0056_0060_C02S3_894583.indd 58 5/7/10 10:07 AM Circular motion Think about a horse’s horizontal motion on a carousel, such as the one in Figure 17. The horse moves in a circular path. Its speed remains constant, but it is accelerating because its direction of motion changes. The change in the direction of the horse’s velocity is toward the center of the carousel. The horse’s velocity is perpendicular to the inward acceleration. Acceleration toward the center of a curved or circular path is called centripetal acceleration. In the same way, Earth experiences centripetal acceleration as it orbits the Sun in a nearly circular path. Reading Check Define the term centripetal acceleration. Projectile motion If you have tossed a ball to someone, you have probably noticed that thrown objects do not travel in straight lines. They curve downward. That is why quarterbacks, dart players, and archers aim above their targets. Anything that is thrown or shot through the air is called a projectile. Earth’s gravity causes projectiles to follow a curved path. ■ Figure 17 The horizontal speed of the horses in this carousel is constant, but the horses are accelerating because their direction is changing constantly. The acceleration of each horse is toward the center of the circular carousel. Horizontal and vertical motion When you throw or shoot an object, such as the rubber band in Figure 18, the force exerted by your hand gives the object a horizontal velocity. For example, after releasing the rubber band, its horizontal velocity is constant. The rubber band does not accelerate horizontally. If there were no gravity, the rubber band would move along the straight dotted line in Figure 18. However, when you release a rubber band, gravity causes it to accelerate downward. The rubber band has an increasing vertical velocity. The result of these two motions is that the rubber band travels in a curve, even though its horizontal and vertical motions are completely independent of each other. vh = 2.0 m/s VOCABULARY ACADEMIC VOCABULARY Constant not varying or changing over time; a quantity that does not vary The constant hum of the fan made it difficult to sleep. vh = 2.0 m/s vv = 0.0 m/s vh = 2.0 m/s vv = 0.5 m/s vv = 1.0 m/s ■ Figure 18 The student gives the rubber band a horizontal velocity. The horizontal velocity of the rubber band remains constant, but gravity causes the rubber band to accelerate downward. The combination of these two motions causes the rubber band to move in a curved path. Section 3 • Acceleration 0056_0060_C02S3_894583.indd 59 59 5/7/10 10:07 AM Throwing and dropping If you were to throw a ball as hard as you could in a perfectly horizontal direction, would it take longer to reach the ground than if you dropped a ball from the same height? Surprisingly, it will not. A thrown ball and a dropped ball will hit the ground at the same time. Both balls in Figure 19 travel the same vertical distance in the same amount of time. However, the ball thrown horizontally travels a greater horizontal distance than the ball that is dropped. ■ Figure 19 The dropped ball and the thrown ball in this multiflash photograph have the same downward acceleration. Concepts in Motion Animation Section 3 Amusement park acceleration Riding roller coasters in amusement parks can give you the feeling of danger, but these rides are designed to be safe. Engineers use the laws of physics to design amusement park rides that are thrilling but harmless. Roller coasters are constructed of steel or wood. Because wood is not as strong as steel, wooden roller coasters do not have hills that are as high and as steep as some steel roller coasters have. The highest speeds and accelerations are usually produced on steel roller coasters. Steel roller coasters can offer multiple steep drops and inversion loops, which give the rider large accelerations. As riders move down a steep hill or an inversion loop, they will accelerate toward the ground due to gravity. When riders go around a sharp turn, they are also accelerated. This acceleration makes them feel as if a force is pushing them toward the side of the car. Review Section Summary ◗ Acceleration is the rate of change of velocity. ◗ The speed of an object increases if the acceleration is in the same direction as the velocity. ◗ The speed of an object decreases if the acceleration and the velocity of the object are in opposite directions. ◗ If an object is moving in a straight line, the size of the change in velocity equals the final speed minus the initial speed. ◗ Acceleration toward the center of a curved or circular path is called centripetal acceleration. SC.912.P.12.2, MA.912.S.1.2 25. MAIN Idea Describe the acceleration of your bicycle as you ride it from your home to the store. 26. Determine the change in velocity of a car that starts at rest and has a final velocity of 20 m/s north. 27. Describe the motion of an object that has an acceleration of 0 m/s2. 28. Think Critically Suppose a car is accelerating so that its speed is increasing. First, describe the line that you would plot on a speedtime graph for the motion of the car. Then describe the line that you would plot on a distance-time graph. Apply Math 29. Calculate Time A ball is dropped from a cliff and has an acceleration of 9.8 m/s2. How long will it take the ball to reach a speed of 24.5 m/s? 30. Calculate Speed A sprinter leaves the starting blocks with an acceleration of 4.5 m/s2. What is the sprinter’s speed 2 s later? 60 Chapter 2 • Motion 0056_0060_C02S3_894583.indd 60 Assessment Online Quiz 5/7/10 10:07 AM LAB Motion Graphs SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following: bar graphs, line graphs, stem and leaf plots, circle graphs, histograms, box and whisker plots, scatter plots, cumulative frequency (ogive) graphs. Objectives n Measure the position of a moving object. n Create a distance-time graph. n Use a distance-time graph to explain how an object is changing speeds. Background: Cars are equipped with speedometers that allow the driver to monitor the car’s speed. Toy cars, however, do not have speedometers. How would you determine the speed of a toy car? In this activity, you will graph the motion of a toy car. Your distance-time graph will allow you to determine whether the toy car is speeding up, slowing down, or moving at a constant speed. Question: How is the changing speed of an object represented on a distance-time graph? Preparation 6. Use the camera to record a video of the toy car’s motion. 7. Set the camera to play the video frame by frame. Replay the video for 0.5 s, stopping to take a measurement every 0.1 s. 8. Determine the toy car’s position for each 0.1 s time interval by reading the meterstick in the video. Record it in the data table. Materials Conclude and Apply camera with video capabilities windup toy car meterstick 1. Draw a distance-time graph for the toy car using the data that you collected. 2. Calculate the toy car’s speed for each interval. 3. Rank the speeds of each 0.1 s interval. On your graph, label the fastest as 1 and the slowest as 5. 4. Identify when the toy car’s speed increased, decreased, and remained constant. (Hint: How does the slope of the line change between intervals?) 5. Infer how you might use a distance-time graph to check that a car’s speedometer is working. Safety Precautions Procedure 1. Read the procedure and safety information, and complete the lab form. 2. Make a data table to record the position and speed of the toy car every 0.1 s. 3. Mark a starting line on the lab table or the surface recommended by your teacher. 4. Place a meterstick parallel to the path that the toy car will take. Have one of the members of your group get ready to operate the camera. 5. Place the toy car at the starting line. ? Inquiry 0061_0063_C02L1_894583.indd 61 Lab YOUR DATA Compare your graph to those made by your classmates. Discuss possible reasons why the graphs might be different. Chapter 2 • Lab 61 5/7/10 10:09 AM LAB The Momentum of Colliding Objects SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following: bar graphs, line graphs, stem and leaf plots, circle graphs, histograms, box and whisker plots, scatter plots, cumulative frequency (ogive) graphs. Objectives Safety Precautions n Observe and calculate the momentum of different balls. n Compare the results of collisions involving different amounts of momentum. Background: In bowling, the ball’s momentum is very important. The bowler must ensure that the ball will travel toward the pins and not into the gutter. The size of the momentum also matters. If the momentum is too small, the ball will knock over very few pins. Question: How do the mass and velocity of a moving object affect its momentum? Preparation Materials meterstick softball tennis ball masking tape trough 62 Chapter 2 • Motion 0061_0063_C02L1_894583.indd 62 stopwatch racquetball baseball balance Procedure Make a Plan 1. Read the procedure and safety information, and complete the lab form. 2. Copy the data table. 3. Use the balance to measure the mass of the racquetball, tennis ball, and baseball. Record these masses in your data table. 4. Measure a 2-m distance on the floor, and mark it with two pieces of masking tape. Arrange the trough so that it begins at one line of tape and extends about a meter beyond the other line of tape. 5. Place the softball in the trough over the piece of tape. Starting from the other piece of tape, slowly roll the racquetball along the trough toward the softball. ? Inquiry Lab 5/7/10 10:09 AM Data Table Action Time Velocity Mass Momentum Distance Softball Moved Racquetball rolled slowly Racquetball rolled quickly Tennis ball rolled slowly Tennis ball rolled quickly Baseball rolled slowly Baseball rolled quickly 6. Use a stopwatch to time how long it takes the racquetball to roll the 2-m distance and hit the softball. Record this time in your data table. 7. Measure and record the distance that the softball moved. 8. Repeat steps 5–7, rolling the racquetball quickly. 9. Repeat steps 5–7, rolling the tennis ball slowly and then quickly. 10. Repeat steps 5–7, rolling the baseball slowly and then quickly. Concllud de and d Apply Apply Conclude 1. Infer from your graph how the distance that the softball moves after each collision depends on the momentum of the ball that hits it. 2. Describe How do an object’s velocity and mass affect the amount of momentum that it has? 3. Explain why bowling balls have such a large mass. What would happen if you tried to bowl with a table tennis ball? Explain. 4. Infer When you bowl, should you roll the ball gently? Explain. Analyze Your Data 1. Calculate the momentum of the rolled ball for each trial using the formula p = mv. Record your calculations in the data table. 2. Graph the relationship between the momentum of each ball and the distance that the softball moved. The x-axis should be momentum (kg·m/s), and the y-axis should be distance (m). YOUR DATA Make a Graph As a class, make a momentumdistance graph using data from everyone in the class. Discuss how this graph is similar to and different from the graphs made by individual groups. Chapter 2 • Lab 0061_0063_C02L1_894583.indd 63 63 5/7/10 10:09 AM No Driver? No Worries! SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. SC.912.N.4.1: Explain how scientiﬁc knowledge and reasoning provide an empirically-based perspective to inform society’s decision making. he diesel-powered car nicknamed Stanley faced a difficult mission—drive more than 200 km across the Mojave Desert in less than ten hours, navigating narrow tunnels, dozens of sharp turns, and a winding mountain pass with sheer drops on each side. The real challenge? Stanley, shown in Figure 1, was not allowed to have a driver. T Grand challenge This was the setting for the 2005 DARPA (Defense Advanced Research Projects Agency) Grand Challenge, a competition won by Stanley and the Stanford Racing Team. The competition was part of an ongoing effort to develop autonomous ground vehicles—vehicles that drive and navigate without a remote control or a human driver. Using autonomous vehicles in combat situations keeps soldiers off the battlefield and protects lives. Physics at the wheel How can a car drive itself? To drive safely, it must interpret the environment, evaluate its position relative to the destination, navigate obstacles, and control speed and direction of motion. Light beams emitted by lasers and radio waves given off by a radar unit bounce off surrounding objects and geographical features. Reflection times determine distances between the car and these objects and help evaluate changes in position and terrain. Additional position data is provided by the Global Positioning System (GPS) and sensors that measure wheel rotation and direction of motion. Stanley’s sophisticated computer integrates all incoming data, compares it to a map of the route, and makes necessary adjustments in steering, throttling, and braking. 64 Figure 1 Stanley, an autonomous vehicle designed by a team from Stanford University, won the 2005 DARPA Grand Challenge. Eliminating dangerous driving Is this technology useful in the civilian world? Human drivers face many distractions. Factors like cell phone use and unexpected traffic situations contribute to almost 40,000 deaths in U.S. traffic accidents each year. But autonomous cars would not be distracted and could make rapid course and speed adjustments and reduce accidents. Participants in the 2007 DARPA Urban Challenge proved that autonomous cars could function in a city setting. This competition required complex maneuvers like merging into traffic, parking, negotiating stop signs, and rerouting around unexpected roadblocks. Ultimately, cars like Stanley could save lives on the battlefield and in our communities. WebQuest Design an Advertisement Brainstorm the potential benefits of using automated cars in a city setting. Use your ideas to design a poster to advertise an automated car service. Share your poster with the class. Chapter 2 • Motion 0064_C02ITF_894583.indd 64 5/3/10 12:17 PM 2 THEME FOCUS Motion and Forces The motion of an object can be described by the distance it travels, its displacement, speed, velocity, momentum, and acceleration. BIG Idea Motion occurs when an object changes its position. Section n 1 Describing Motion displacement (p. 45) motion (p. 44) speed (p. 46) MAIN Idea Position describes where an object is, and speed describes how fast the object is moving. • Motion occurs when an object changes its position relative to a reference point. • Displacement is the distance and direction of a change in position from the starting point. • Speed is the rate at which an object’s position changes. • On a distance-time graph, time is the x-axis and distance is y-axis. • The slope of a line plotted on a distance-time graph is the speed. Section n 2 Velocity and Momentum momentum (p. 54) velocity (p. 51) MAIN Idea An object’s velocity describes the object’s speed and direction of motion. • The velocity of an object includes the object’s speed and its direction of motion relative to a reference point. • An object’s motion is always described relative to a reference point. • The momentum of an object is the product of its mass and velocity: p = mv. Section n 3 Acceleration acceleration (p. 56) centripetal acceleration (p. 59) Review 0065_C02SG_894583.indd 65 Vocabulary eGames MAIN Idea Acceleration describes how the velocity of an object is changing with time. • Acceleration is the rate of change of velocity. • The speed of an object increases if the acceleration is in the same direction as the velocity. • The speed of an object decreases if the acceleration and the velocity of the object are in opposite directions. • If an object is moving in a straight line, the size of the change in velocity equals the final speed minus the initial speed. • Acceleration toward the center of a curved or circular path is called centripetal acceleration. Chapter 2 • Study Guide 65 5/3/10 12:19 PM 2 SC.912.P.12.2, MA.912.S.1.2 Use Vocabulary Compare and contrast the following pairs of terms. 31. speed—velocity 32. motion—displacement 33. velocity—momentum 34. acceleration—velocity Check Concepts 35. Which of the following do you calculate when you divide the total distance traveled by the total travel time? A) average speed B) constant speed C) variable speed D) instantaneous speed 36. Which of the following is the SI unit of acceleration? A) s/km2 B) km/h C) m/s2 D) cm/s 37. Which of the following is not used in calcu- lating acceleration? A) initial velocity B) average speed C) time interval D) final velocity 38. A car, a bicycle, a mouse, and a bug have the same velocity. Which has the greatest momentum? A) the car B) the bicycle C) the mouse D) the bug 66 Chapter 2 • Motion 0066_0067_C02CR_894583.indd 66 39. In which of the following conditions does the car not accelerate? A) A car moves at 80 km/h on a flat, straight highway. B) The car slows from 80 km/h to 35 km/h. C) The car turns a corner. D) The car speeds up from 35 km/h to 80 km/h. 40. How is speed defined? A) acceleration/time B) change in velocity/time C) distance/time D) displacement/time 41. Which best describes why projectiles move in a curved path? A) They have constant horizontal velocity and vertical acceleration. B) They have horizontal acceleration and constant vertical velocity. C) They have horizontal momentum and constant vertical velocity. D) They have horizontal acceleration and vertical momentum. Interpret Graphics Use the table below to answer question 42. Distance-Time for Runners Time (s) 1 2 3 4 Sally’s distance (m) 2 4 6 8 Alonzo’s distance (m) 1 2 2 4 42. Make a distance-time graph that shows the motion of both runners. What is the average speed of each runner? Which runner stops briefly? Over what time interval do they both have the same speed? Assessment Online Test Practice 5/3/10 12:22 PM 2 43. Copy and complete this concept map on motion. THEME FOCUS Interactive Concept Map Concepts in Motion A pply Math 49. Calculate Speed A cyclist must travel 800 km. How many days will the trip take if the cyclist travels 8 h/day at an average speed of 16 km/h? Motion can be described by 50. Calculate Acceleration A satellite’s speed is velocity which is a change in position which includes c. d. which equals b. which equals change in velocity time distance time Think Critically 44. Explain Why is knowing only a hurricane’s speed not enough information to be able to warn people to evacuate? 45. Evaluate Which of the following represents the greatest speed: 20 m/s, 200 cm/s, or 0.2 km/s? 46. Recognize Acceleration can occur when a car is moving at constant speed. What must cause this acceleration? 47. BIG Idea Determine If you walked 20 m, took a book from a table, and walked back to your seat, what are the distance you traveled and your displacement? 48. Explain When you are describing the rate that a race car goes around a track, should you use the term speed or velocity to describe the motion? Assessment 0066_0067_C02CR_894583.indd 67 Online Test Practice 5,000 m/s. After 1 min, it is 10,000 m/s. What is the satellite’s acceleration? 51. Calculate Displacement A cyclist leaves home and rides due east for a distance of 45 km. She returns home on the same bike path. If the entire trip takes 4 h, what is her average speed? What is her displacement? 52. Calculate Velocity The return trip of the cyclist in question 51 took 30 min longer than her trip east, although her total time was still 4 h. What was her velocity in each direction? Use the figure below to answer question 53. Runners’ Motion 60 Distance (m) a. 50 40 Runner #1 Runner #2 30 20 10 0 1 2 3 4 5 6 7 8 Time (s) 53. Interpret a Graph Use the graph to determine which runner had the greater speed. 54. Calculate Mass Find the mass of a car that has a speed of 30 m/s and a momentum of 45,000 kg·m/s. Chapter 2 • Review 67 5/3/10 12:22 PM Standardized Test Practice Multiple Choice Record your answers on the answer sheet provided by your teacher or on a sheet of paper. 1. If the speed of sound during a thunderstorm is 330 m/s, how long does it take for the sound SC.912.P.12.2 of thunder to travel 1485 m? A. 45 s C. 4900 s B. 4.5 s D. 0.22 s Use the figure below to answer questions 2–4. Speed Changing over Distance 30 5. A skier is going down a hill at a speed of 9 m/s. The hill gets steeper and her speed increases to 18 m/s in 3 s. What is her SC.912.P.12.2 acceleration? 2 2 A. 9 m/s C. 27 m/s 2 B. 3 m/s D. 6 m/s2 6. Which of the following best describes an object with constant velocity? A. It is changing direction. B. Its acceleration is increasing. C. Its acceleration is zero. D. Its acceleration is negative. SC.912.P.12.2 Speed (km/h) 25 Use the table below to answer questions 7–9. 20 Runner 15 Ling-Ling LaToya 10 Bill José 5 0 1 2 3 4 2. The graph shows how a cyclist’s speed changed over a 0.25-h trip. What is the SC.912.P.12.2 cyclist’s average speed? A. 2 km/h C. 20 km/h B. 30 km/h D. 8 km/h 3. Once the trip was started, how many times SC.912.P.12.2 4. What was the fastest speed that the cyclist traveled? A. 20 km/h B. 30 km/h C. 12 km/h D. 10 km/h 68 Standardized Test Practice 0068_0069_C02STP_894583.indd 68 Time (min) 10.5 8.9 42 38 32 30 5 Distance (km) did the cyclist stop? A. 0 C. 2 B. 4 D. 5 Distance Covered (km) 12.5 7.8 SC.912.P.12.2 7. What is Ling-Ling’s average speed? A. 0.3 km/min C. 3.0 km/min B. 530 km/min D. 3.4 km/min SC.912.P.12.2 8. Which runner has the fastest average speed? A. Ling-Ling C. Bill SC.912.P.12.2 B. LaToya D. José 9. If all four runners have the same mass, who has the smallest momentum? A. Ling-Ling C. Bill B. LaToya D. José SC.912.P.12.2 10. The movement of the Australian plate pushes Australia north at an average speed of about 17 cm per year. What will Australia’s displacement be in meters in 1,000 years? A. 170 m north C. 1,700 m north B. 170 m south D. 1,700 m south SC.912.P.12.2 Assessment Standardized Test Practice 5/3/10 12:18 PM Short Response Extended Response Record your answers on the answer sheet provided by your teacher or on a sheet of paper. Record your answers on a sheet of paper. 14. Describe three ways that your velocity could change as you jog along a park’s path. Use the figure below to answer questions 11 and 12. SC.912.P.12.2 Distance-Time Graph 2,400 15. Where would you place the location of a ref- erence point in order to describe the motion of a space probe traveling from Earth to Jupiter? Explain your choice. SC.912.P.12.2 2,200 2,000 1,800 Swimmer C Distance (m) 1,600 16. Two cars approach each other. How does the 1,400 Swimmer B speed of one car relative to the other compare with speed of each car relative to the ground? SC.912.P.12.2 1,200 1,000 800 Swimmer A 600 Use the figure below to answer question 17. 400 v = 13 m/s 200 0 10 20 30 Time (min) 11. The graph shows the motion of three swim- mers during a 30-min workout. Which swimmer had the highest average speed over the 30-min time interval? Explain. SC.912.P.12.2 17. Two balls are at the same height and released 12. Did all of the swimmers swim at a constant speed? Explain how you know. at the same time. One ball is dropped and hits the ground 5 s later. The other initially moves horizontally. When does the second ball hit the ground? How far does it travel SC.912.P.12.2 horizontally? SC.912.P.12.2 13. If a car has a velocity of 40 km/h west and then comes to a stop in 5 s, what is its accelSC.912.P.12.2 eration in m/s2? NEED EXTRA HELP? If You Missed Question . . . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Review Section . . . 1 1 1 1 3 3 1 1 2 2 1 1 3 3 2 2 3 Assessment 0068_0069_C02STP_894583.indd 69 Standardized Test Practice Standardized Test Practice 69 5/3/10 12:18 PM CHAPTER 3 Forces and Newton’s Laws Your one-stop online resource connectED.mcgraw-hill.com ? Video WebQuest Audio Assessment Review Concepts in Motion g Inquiry Multilingual eGlossary Launch Lab Force, Mass, and Acceleration You have probably noticed that it is more difficult to lift a bookbag containing three books than it is to lift a bookbag containing one book. What effect does mass have on how much force is needed to change an object’s motion? For a lab worksheet, use your StudentWorks™ Plus Online. ? Inquiry Launch Lab Make a three-tab book. Label it as shown. Use it to organize your notes on Newton’s laws of motion. 1st law 2nd law 3rd law of motion of motion of motion Newton’s Laws 0070_0071_C03CO_894583.indd 70 5/3/10 11:49 AM THEME FOCUS Motion and Forces Section 1 • Forces Objects that interact exert forces on each other. Section 2 • Newton’s Laws of BIG Idea A force is a push or pull. Motion Section 3 • Using Newton’s Laws Chapter 3 • Forces and Newton’s Laws 0070_0071_C03CO_894583.indd 71 71 5/3/10 11:50 AM Section 1 SC.912.P.10.10: Compare the magnitude and range of the four fundamental forces (gravitational, electromagnetic, weak nuclear, strong nuclear). SC.912.P.12.4: Describe how the gravitational force between two objects depends on their masses and the distance between them. SC.912.N.1.6: Describe how scientiﬁc inferences are drawn from scientiﬁc observations and provide examples from the content being studied. ALSO COVERS: MA.912.S.1.2. Reading Preview Forces Essential Questions MAIN Idea Unbalanced forces change motion. ◗ How are force and motion Real-World Reading Link Have you ridden a bike down a steep hill? You might have noticed that you went faster and faster or that you had to brake very hard to stop the bike. In both cases, you and your bike were accelerating. What caused that acceleration? related? ◗ How is the net force on an object determined? ◗ Why is there friction between objects? ◗ What is the difference between mass and weight? Review Vocabulary mass: amount of matter in an object New Vocabulary force net force friction gravity field weight g Multilingual eGlossary What is force? Catching a basketball and hitting a baseball with a bat are examples of applying force to an object. A force is a push or a pull. In both examples, the applied force changes the movement of the ball. Sometimes, it is obvious that a force has been applied. But other forces are not as noticeable. For instance, are you conscious of the force that the floor exerts on your feet? Can you feel the force of the atmosphere pushing against your body or gravity pulling on your body? Think about all of the forces that you exert in a day. Every push, pull, stretch, or bend results in a force being applied to an object. Changing motion What happens to the motion of an object when you exert a force on it? A force can cause the motion of an object to change. Think of kicking a soccer ball, as shown in Figure 1. The player’s foot strikes the ball with a force that causes the ball to stop and then move in the opposite direction. If you have played billiards, you know that you can force a ball at rest to roll into a pocket by striking it with another ball. The force of the moving ball causes the ball at rest to move in the direction of the force. In each case, the velocity of the ball was changed by a force. ■ Figure 1 When the player kicks the soccer ball, she is exerting a force on the ball. This kick will cause the ball’s motion to change. 72 Chapter 3 • Forces and Newton’s Laws 0072_0079_C03S1_894583.indd 72 5/7/10 9:59 AM Net force When two or more forces act on an object at the same time, the forces combine to form the net force. The net force is the sum of all of the forces acting on an object. Forces have a direction, so they follow the same addition rules as displacement, as listed in Table 1. Forces are measured in the SI unit of newtons (N). A force of about 3 N is needed to lift a full can of soda at a constant speed. Unbalanced forces Look at Figure 2A. The students are each Table 1 Rules for Adding Forces 1. Add forces in the same direction. 2. Subtract forces in opposite directions. 3. Forces not in the same direction or in opposite directions cannot be directly added together. pushing on the box in the same direction. These forces are combined, or added together, because they are exerted on the box in the same direction. The students in Figure 2B are pushing in opposite directions. Here, the direction of the net force is the same as the direction of the larger force. In other words, the student who pushes harder causes the box to move in the direction of that push. The net force will be the difference between the two forces because they are in opposite directions. In Figure 2A and Figure 2B, the net force had a value that was not zero and the box moved. The forces that the students applied are considered unbalanced forces. ? Inquiry Video Lab Balanced forces Now suppose that the students were pushing with the same size force but in opposite directions, as shown in Figure 2C. The net force on the box is zero because the two forces cancel each other. Forces on an object that are equal in size and opposite in direction are called balanced forces. Unbalanced forces cause changes in motion. Balanced forces do not cause a change in motion. + = Net Force = [A] These students are pushing on the box in the same direction. These forces are unbalanced. The net force is the sum of the two forces, and the box will move in the direction that the students push. + = Net Force = [B] These students are pushing on the box with unequal forces in opposite directions. These forces are unbalanced. The net force is the difference of the two forces, and the box will move in the direction of the larger force. ■ Figure 2 Forces can be balanced or unbalanced. Identify another example of unbalanced forces and another example of balanced forces. + = 0 Net Force = 0 [C] These students are pushing on the box with equal forces but in opposite directions. These forces are balanced. The net force is zero and the box does not move. Section 1 • Forces 0072_0079_C03S1_894583.indd 73 73 5/7/10 9:59 AM Friction Suppose you give a skateboard a push with your hand. After you let go, the skateboard slows down and eventually stops. Because the skateboard’s motion is changing as it slows down, there must be a force acting on it. The force that slows the skateboard is called friction. Friction is the force that opposes the sliding motion of two surfaces that are touching each other. What causes friction? Would you believe that the surface of a highly polished piece of metal is rough? Surfaces that appear smooth actually have many bumps and dips. These bumps and dips can be seen when the surface is examined under a microscope, as shown in Figure 3. If two surfaces are in contact, welding or sticking occurs where the bumps touch each other. These microwelds are the source of friction. To move one surface over the other, a force must be applied to break the microwelds. Reading Check Describe the source of friction. ■ Figure 3 The surface of this tea- pot looks and feels smooth, but it is rough at the microscopic level. The amount of friction between two surfaces depends on the kinds of surfaces and the force pressing the surfaces together. Rougher surfaces have more bumps and can form more microwelds, increasing the amount of friction. In addition, a larger force pushing the two surfaces together will cause more of the bumps to come into contact, as shown in Figure 4. The microwelds will be stronger, and a greater force must be applied to the object to break the microwelds. Static friction Suppose you have a cardboard box filled with books, such as the one in Figure 5, and want to move that box. The box is resting on what seems to be a smooth floor, but when you push on the box, it does not budge. The box experiences no change in motion, so the net force on the box is zero. The force of friction cancels your push. More force Force ■ Figure 4 Friction is caused by microwelds that form between two surfaces. Microwelds are stronger when the two surfaces are pushed together with a larger force. Explain how the area of contact Surfaces Microwelds form where bumps come into contact. Same two surfaces More force presses the bumps closer together. between the surfaces changes when they are pushed together. 74 Chapter 3 • Forces and Newton’s Laws 0072_0079_C03S1_894583.indd 74 5/7/10 9:59 AM Applied force Applied force Static friction Sliding friction Static friction balances the applied force. The box remains at rest and does not accelerate. Sliding friction and the applied force are unbalanced. The box accelerates to the right. This type of friction is called static friction. Static friction prevents two surfaces from sliding past each other and is due to the microwelds that have formed between the bottom of the box and the floor. Your push is not large enough to break the microwelds, and the box does not move, as shown in Figure 5. Sliding friction If you and a friend push together, as shown on the right in Figure 5, the box moves. Together, you and your friend have exerted enough force to break the microwelds between the floor and the bottom of the box. But if you stop pushing, the box quickly comes to a stop. To keep the box moving, you must continually apply a force. This is because sliding friction opposes the motion of the box as the box slides across the floor. Sliding friction opposes the motion of two surfaces sliding past each other and is caused by microwelds constantly breaking and forming as the objects slide past each other. The force of sliding friction is usually smaller than the force of static friction. Rolling friction You may think of friction as a disadvantage. But wheels, like the ones shown in Figure 6, would not work without friction. As a wheel rolls, static friction acts over the area where the wheel and surface are in contact. This special case of static friction is sometimes called rolling friction. You may have seen a car that was stuck in snow, ice, or mud. The driver steps on the gas, but the wheels just spin without the car moving. The force used to rotate the tires is larger than the force of static friction between the wheels and the ground, so the tires slide instead of gripping the ground. Spreading sand or gravel on the surface increases the friction until the wheels stop slipping and begin rolling. When referring to tires on vehicles, people often use the term traction instead of friction. ■ Figure 5 Friction opposes the sliding motion of two surfaces that are touching each other. Describe the net force on each box. VOCABULARY WORD ORIGIN Friction from the Latin fricare meaning “to rub” Oil can be used to reduce friction. ■ Figure 6 Rolling friction between the in-line skate’s wheels and the pavement keeps the wheels from slipping. Rolling friction Wheel rotation Section 1 • Forces 0072_0079_C03S1_894583.indd 75 75 5/7/10 9:59 AM Gravity ? Inquiry MiniLab Compare Friction and Gravity Procedure 1. Read the procedure and safety information, and complete the lab form. 2. Place an ice cube, a rock, an eraser, a wood block, and a square of aluminum foil at one end of a metal or plastic tray. 3. Slowly lift the end of the tray with the items. 4. Have a partner use a metric ruler to measure the height of the raised end of the tray at which each object begins to slide. Record the measurements. Analysis 1. Create a table and include the height at which each object began to slide. 2. Infer Which item experienced the greatest frictional force? How do you know? 3. Identify the force that caused the objects to slide. At this moment, you are exerting an attractive force on everything around you—your desk, your classmates, and even the planet Jupiter, millions of kilometers away. This attractive force acts on all objects with mass and is called gravity. Gravity is an attractive force between any two objects that depends on the masses of the objects and the distance between them. Gravity is one of the four basic forces. These forces are called the fundamental forces. The other basic forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force. Gravity acts on all objects with mass, and the electromagnetic force acts on all charged particles. Both gravity and the electromagnetic force have an infinite range. The nuclear forces only affect particles in the nuclei of atoms. The law of universal gravitation In the 1660s, British scientist Isaac Newton used data on the motions of the planets to find the relationship between the gravitational force between two objects, the objects’ masses, and the distance between them. This relationship is called the law of universal gravitation and can be written as the following equation. mm d 1 2 F = G_ 2 In this equation, G is the universal gravitational constant, and d is the distance between the centers of the two masses, m 1 and m 2. The law of universal gravitation states that the gravitational force increases as the mass of either object increases and as the objects move closer, as shown in Figure 7. The force of gravity between any two objects can be calculated if their masses and the distance between them are known. SC.912.P.12.4: Describe how the gravitational force between two objects depends on their masses and the distance between them. ■ Figure 7 The law of universal gravitation states that the gravitational force between two objects depends on their masses and the distance between them. 76 If the mass of either of the objects increases, the gravitational force between them increases. If the objects are closer together, the gravitational force between them increases. Chapter 3 • Forces and Newton’s Laws 0072_0079_C03S1_894583.indd 76 5/7/10 10:00 AM Gravity and you The law of universal gravitation explains why you feel Earth’s gravity but not the Sun’s gravity or this book’s gravity. While the Sun has much more mass than Earth, the Sun is too far away to exert a noticeable gravitational attraction on you. And while this book is close, it does not have enough mass to exert an attraction that you can feel. Only Earth is both close enough and has a large enough mass that you can feel its gravitational attraction. Review Additional Practice Problems The range of gravity According to the law of universal gravi- tation, the gravitational force between two masses decreases rapidly as the distance between the masses increases. For example, if the distance between two objects increases from 1 m to 2 m, the gravitational force between them becomes onefourth as large. If the distance increases from 1 m to 10 m, the gravitational force between the objects is one-hundredth as large. However, no matter how far apart two objects are, the gravitational force between them never completely goes to zero. Because the gravitational force between two objects never disappears, gravity is called a long-range force. Reading Check Explain why gravity is called a long-range force. The gravitational field Because contact between objects is not required, gravity is sometimes discussed as a field. A field is a region of space that has a physical quantity (such as a force) at every point. All objects are surrounded by a gravitational field. Figure 8 shows that Earth’s gravitational field is strongest near Earth and becomes weaker as the distance from Earth increases. The strength of the gravitational field, represented by the letter g, is measured in newtons per kilogram (N/kg). _ g = 9.8 N kg _ g = 0.98 N kg _ g = 4.9 N kg _ g = 7.4 N kg _ g = 2.5 N kg ■ Figure 8 Earth’s gravitational field exists at all points in space. It is strongest near the surface and decreases in strength as one moves away from Earth. Section 1 • Forces 0072_0079_C03S1_894583.indd 77 77 5/7/10 10:00 AM Weight The gravitational force exerted on an object is the object’s weight. The universal law of gravitation can be used to calculate weight, but scientists use a simplified version of this equation that combines m 1, d 2, and G into a single number called the gravitational strength, g. Weight of Common Table 2 Objects on Earth Object Weight Cell phone Backpack full of books Jumbo jet Weight Equation 1N weight (N) = mass (kg) × gravitational strength (N/kg) F g = mg 100 N 3.4 million N We use Fg for weight because weight is the force due to gravity. Weight has units of newtons (N) because it is a force. The g in the subscript stands for gravity. The gravitational strength, g, has the units N/kg. Recall that 1 N = 1 kg ∙ m/s2. So, g can also be written with units of m/s2. Weight and mass Weight and mass are not the same. Weight is a force, and mass is a measure of the amount of matter an object contains. But, according to the weight equation, weight and mass are related. Weight increases as mass increases. SC.912.P.12.4: Describe how the gravitational force between two objects depends on their masses and the distance between them. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. Weight on Earth We often need to know an object’s weight on Earth. Near Earth’s surface, m 1, from the law of universal gravitation, is Earth’s mass and d is Earth’s radius. As a result, g = 9.8 N/kg. Table 2 lists the weights of some objects on Earth. EXAMPLE Problem 1 Solve for Weight An elephant has a mass of 5,000 kg. What is the elephant’s weight? Identify the Unknown: weight: F g List the Knowns: mass: m = 5,000 kg gravitational strength: g = 9.8 N/kg Set Up the Problem: F g = mg Solve the Problem: F g = (5,000 kg)(9.8 N/kg) = 49,000 N Check the Answer: The gravitational strength is about 10 N/kg, so we would expect the elephant’s weight to be about 50,000 kg. Our answer (F g = 49,000 N) makes sense. PRACTICE Problems Find Additional Practice Problems in the back of your book. 1. A squirrel has a mass of 0.5 kg. What is its weight? 2. A boy weighs 400 N. What is his mass? Review Additional Practice Problems 3. Challenge An astronaut has a mass of 100 kg and has a weight of 370 N on Mars. What is the gravitational strength on Mars? 78 Chapter 3 • Forces and Newton’s Laws 0072_0079_C03S1_894583.indd 78 5/7/10 10:00 AM Weight away from Earth An object’s weight usually refers to the gravitational force between the object and Earth. But the weight of an object can change, depending on the gravitational force on the object. For example, the gravitational strength on the Moon is 1.6 N/kg, about one-sixth as large as Earth’s gravitational strength. As a result, a person, such as the astronaut in Figure 9, would weigh only about one-sixth as much on the Moon as on Earth. Finding other planets Earth’s motion around the Sun is affected by the gravitational pulls of the other planets in the solar system. In the same way, the motion of every planet in the solar system is affected by the gravitational pulls of all of the other planets. In the 1840s, the most distant planet known was Uranus. The motion of Uranus calculated from the law of universal gravitation disagreed slightly with its observed motion. Some astronomers suggested that there must be an undiscovered planet affecting the motion of Uranus. Using the law of universal gravitation and the laws of motion, two astronomers independently calculated the orbit of this planet. As a result of these calculations, the planet Neptune was found in 1846. Section 1 Review Section Summary ◗ A force is a push or a pull on an object. ◗ The net force on an object is the combina- tion of all of the forces acting on the object. ◗ Unbalanced forces cause the motion of objects to change. ◗ Friction is the force that opposes the slid- ing motion of two surfaces that are in contact. ◗ Gravity is an attractive force between all objects that have mass. ■ Figure 9 Although the astronaut has the same mass on the Moon, he weighs less than he does on Earth. He can take longer steps and jump higher than on Earth. SC.912.P.12.4, MA.912.S.1.2 4. Describe two forces that would change the motion of a bicycle traveling along a road. MAIN Idea 5. Explain Can there be forces acting on an object if the object is at rest? Must there be an unbalanced force acting on a moving object? Explain your answers. 6. Explain Why does coating surfaces with oil reduce friction between the surfaces? 7. Distinguish between the mass of an object and the object’s weight. 8. Think Critically Suppose Earth’s mass increased but Earth’s diameter did not change. How would the gravitational strength near Earth’s surface change? Apply Math 9. Calculate Weight On Earth, what is the weight of a large-screen TV that has a mass of 75 kg? 10. Calculate Net Force Two students push on a box in the same direction, and one student pushes in the opposite direction. What is the net force on the box if each student pushes with a force of 50 N? Assessment 0072_0079_C03S1_894583.indd 79 Online Quiz Section 1 • Forces 79 5/7/10 10:00 AM Section 2 SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. ALSO COVERS: MA.912.S.1.2 Reading Preview Newton’s Laws of Motion Essential Questions MAIN Idea Newton’s laws of motion relate the change in an ◗ What is inertia and how is it related to Newton’s first law of motion? ◗ How can an object’s acceleration be calculated using Newton’s second law of motion? ◗ According to Newton’s third law of motion, how are the forces between interacting objects related? Review Vocabulary acceleration: rate of change of velocity New Vocabulary Newton’s first law of motion inertia Newton’s second law of motion Newton’s third law of motion g Multilingual eGlossary Video BrainPOP ■ Figure 10 You might have seen the law of inertia without even knowing it. For example, as the car hits the block and stops, the red block continues to move forward. Describe another example of inertia. 80 object’s motion with the forces acting on it. Real-World Reading Link Suppose you try to push a wagon and a car with the same amount of force. How will their motions be different? Newton’s laws of motion describe how the wagon and the car will move. Isaac Newton and the Laws of Motion In 1665, Cambridge University in Britain closed for 18 months because of the bubonic plague. Isaac Newton, a 23-year-old student, used this time to develop the law of universal gravitation, calculus, and three laws describing how forces affect the motion of objects. Newton’s laws of motion apply to the motion of everyday objects, such as cars and bicycles, as well as the motion of planets and stars. Newton’s First Law of Motion Recall that forces change an object’s motion. Newton’s first law explains the relationship between force and change in motion. Newton’s first law of motion states that an object moves at a constant velocity unless an unbalanced force acts on it. This means that a moving object will continue to move in a straight line at a constant speed unless an unbalanced force acts on it. If an object is at rest, its velocity is zero and it stays at rest unless an unbalanced force acts on it. Inertia Newton’s first law is sometimes called the law of inertia. Inertia (ih NUR shuh) is the tendency of an object to resist any change in its motion. Figure 10 shows a toy car hitting a block and stopping. The block on top of the car is not attached to the car and keeps traveling. The block’s forward motion demonstrates the property of inertia. Chapter 3 • Forces and Newton’s Laws 0080_0085_C03S2_894583.indd 80 5/7/10 10:12 AM Inertia and mass Does a bowling ball have the same inertia as a table-tennis ball? Why is there a difference? You could not change the motion of a bowling ball much by swatting it with a table-tennis paddle. But you could easily change the motion of the table-tennis ball. A greater force would be needed to change the motion of the bowling ball because it has greater inertia. Recall that mass is the amount of matter in an object. An object’s inertia is related to its mass. The greater an object’s mass is, the greater its inertia is. A bowling ball has more mass than a table-tennis ball has, so the bowling ball has a greater inertia. You will sometimes hear people say that when an object begins to move, inertia is overcome. This is not true. The object still has mass when it is moving, so it still has inertia. As long as the mass is the same, the object has the same inertia. Newton’s Second Law of Motion Newton’s first law of motion states that the motion of an object changes only if an unbalanced force acts on the object. Newton’s second law of motion describes how the forces exerted on an object, its mass, and its acceleration are related. Force and acceleration How are throwing a ball as hard as you can and tossing it gently different? When you throw hard, you exert a greater force on the ball. The ball has a greater velocity when it leaves your hand. The hard-thrown ball has a greater change in velocity, and the change occurs over a shorter period of time. Recall that acceleration equals the change in velocity divided by the time it takes for the change to occur. So, a hard-thrown ball is accelerated more than a gently thrown ball, as shown in Figure 11. ? Inquiry MiniLab Observe Inertia Procedure 1. Read the procedure and safety information, and complete the lab form. 2. Create an inclined plane between 25° and 50° using a board and textbooks. Place a stop block (brick or other heavy object) at the end of the plane. 3. Place a small object in a cart and allow both to roll down the plane. Record the results. 4. Secure the object in the cart with rubber bands (safety belts). Allow both to roll down the plane again. Record the results. Analysis 1. Identify the forces acting on the object in the cart in both runs. 2. Explain why it is important to wear safety belts in a car. SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. 360 m/s2 120 m/s2 50 N 17 N ? Inquiry Virtual Lab ■ Figure 11 According to Newton’s second law of motion, the harder you throw a baseball, the greater its acceleration will be. Section 2 • Newton’s Laws of Motion 0080_0085_C03S2_894583.indd 81 81 5/7/10 10:12 AM ■ Figure 12 If the pitchers apply the same force, the baseball will experience a greater acceleration because it has less mass than the softball. 170 m/s2 240 m/s2 0.20 kg 0.14 kg 34 N 34 N Mass and acceleration If you throw a softball and a baseball as hard as you can, as shown in Figure 12, why do they not have the same speed? The difference is due to their masses. A softball has a mass of about 0.20 kg, but a baseball’s mass is about 0.14 kg. The softball has less velocity after it leaves your hand than the baseball does, even though you exerted the same force. The softball has a smaller final speed because it experienced a smaller acceleration. The acceleration of an object depends on its mass as well as the force exerted on it. Force, mass, and acceleration are related. Reading Check Identify You apply a force of 2 N to a toy car and to a real car. Which car has the greater acceleration? FOLDABLES Incorporate information from this section into your Foldable. Relating force, mass, and acceleration Newton’s second law of motion states an object’s acceleration is in the same direction as the net force on the object and is equal to the net force exerted on it divided by its mass. Newton’s second law can be written as the following equation. The Second Law of Motion Equation net force (in newtons) mass (in kilograms) acceleration (in meters/second2) = __ F net a=_ m In the above equation, acceleration has units of meters per second squared (m/s2) and mass has units of kilograms (kg). Recall that the net force is the sum of all of the forces on an object. Remember that the SI unit for force is a newton (N) and that 1 N = 1 kg∙m/s2. Just like velocity and acceleration, force has a size and a direction. 82 Chapter 3 • Forces and Newton’s Laws 0080_0085_C03S2_894583.indd 82 5/7/10 10:13 AM Calculating net force Newton’s second law can also be used to calculate the net force if mass and acceleration are known. To do this, the equation for Newton’s second law must be solved for the net force, F net. To solve for the net force, multiply both sides of the above equation by the mass. VOCABULARY ACADEMIC VOCABULARY Period a length of time Each class period is 45 minutes. F net m×a=m×_ m The mass, m, on the right side cancels. Fnet = ma For example, when a tennis player hits a ball, the racket and the ball might be in contact for only a few thousandths of a second. Because the ball’s velocity changes over such a short period of time, the ball’s acceleration could be as high as 5,000 m/s2. The ball’s mass is 0.06 kg, so the size of the net force exerted on the ball would be 300 N. Fnet = ma = (0.06 kg)(5,000 m/s2) = 300 kg ∙ m/s2 = 300 N SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. EXAMPLE Problem 2 Solve for Acceleration You push a wagon that has a mass of 12 kg. If the net force on the wagon is 6 N south, what is the wagon’s acceleration? Identify the Unknown: acceleration: a List the Knowns: mass: m = 12 kg net force: F net = 6 N south F Set Up the Problem: net a=_ m Solve the Problem: N south = 0.5 m/s2 south a = 6_ Check the Answer: PRACTICE Problems 12 kg The value of the net force (6) is less than the value of the wagon’s mass (12), so we would expect the acceleration’s value to be less than one. Our answer (0.5 m/s2) makes sense. Find Additional Practice Problems in the back of your book. 11. If a helicopter’s mass is 4,500 kg and the net force on it is 18,000 N upward, what is its acceleration? Review Additional Practice Problems 12. What is the net force on a dragster with a mass of 900 kg if its acceleration is 32.0 m/s2 west? 13. A car pulled by a tow truck has an acceleration of 2.0 m/s2 east. What is the mass of the car if the net force on the car is 3,000 N east? 14. Challenge What is the net force on a sky diver falling with a constant velocity of 10 m/s downward? Section 2 • Newton’s Laws of Motion 0080_0085_C03S2_894583.indd 83 83 5/7/10 10:13 AM Newton’s Third Law of Motion What happens when you push against a wall? If the wall is sturdy, nothing happens. But if you pushed against a wall while wearing roller skates, you would go rolling backward. This is a demonstration of Newton’s third law of motion. Newton’s third law of motion states that when one object exerts a force on a second object, the second object exerts a force on the first that is equal in strength and opposite in direction. Sometimes, Newton’s third law is written as “to every action force there is an equal and opposite reaction force.” However, one force is not causing the second force. They occur at the same time. It does not matter which object is labeled Object 1 and which is labeled Object 2. Think about a boat tied to a dock with a taut rope. You could say that the action force is the boat pulling on the rope and the reaction force is the rope pulling on the boat. But it would be just as correct to say that the action force is the rope pulling on the boat and the reaction force is the boat pulling on the rope. ■ Figure 13 The student pushes on the box, and the box pushes on the student. To understand the motion of each object, the other forces on that object must be examined. Net force = 0 N Force from box, 30 N Static friction, 30 N Forces on the Student 84 Forces on different objects do not cancel If these two forces are equal in size and opposite in direction, you might wonder how some things ever happen. For example, if the box in Figure 13 pushes on the student when the student pushes on the box, why does the box move? According to the third law of motion, action and reaction forces act on different objects. Recall that the net force is the sum of the forces on a single object. The left picture in Figure 13 shows the forces on the student. The net force is zero and the student remains at rest. The right picture shows that there is a net force of 20 N to the right on the box and the box accelerates to the right. Reading Check Explain why the action and reaction forces do not cancel. Net force = 20 N Applied force, 30 N Sliding friction, 10 N Forces on the Box Chapter 3 • Forces and Newton’s Laws 0080_0085_C03S2_894583.indd 84 5/7/10 10:13 AM Forces are interactions Newton’s third law states a very important fact: forces are interactions between objects. For example, it makes no sense to say, “The box has a force of 30 N.” Is this force acting on the box? Is the box pushing on something? What is causing this force? It makes sense, however, to say, “The student applied a force of 30 N to the box.” Furthermore, both objects experience a force from the interaction. Look at the skaters in Figure 14. The male skater is pulling upward on the female skater, while the female skater is pulling downward on the male skater. The two forces are equal in size but opposite in direction. Both skaters feel a pull of the same size. Even if the two objects have different masses, they will feel the same size force. For example, if a bug flies into the windshield of a truck, the bug and the truck exert forces on each other. According to Newton’s third law, the bug and the truck experience the same size force even though their masses and accelerations are different. Section 2 Review Section Summary ◗ Newton’s first law of motion states that the motion of an object at rest or moving with constant velocity will not change unless an unbalanced force acts on the object. ◗ Inertia is the tendency of an object to resist a change in motion. ◗ Newton’s second law of motion states that the acceleration of an object depends on its mass and the net force exerted on it. ■ Figure 14 The skaters exert forces on each other. According to Newton’s third law of motion, the two forces are equal in size but opposite in direction. Both skaters feel the same amount of force. SC.912.P.12.3, MA.912.S.1.2 15. MAIN Idea Describe Use Newton’s laws of motion to describe what happens when you kick a soccer ball. 16. Explain why Newton’s first law of motion is sometimes called the law of inertia. 17. Determine whether the inertia of an object changes as the object’s velocity changes. 18. Explain why an object with a smaller mass has a larger acceleration than an object with a larger mass if the same force acts on each. 19. Think Critically You push a book across a table. The book moves at a constant speed, but you do not move. Identify all of the forces on you. Then, identify all of the forces on the book. ◗ According to Newton’s third law of motion, when an object exerts a force on a second object, the second object exerts a force on the first object. Apply Math 20. Calculate Acceleration A student pushes on a 5-kg box with a force of 20 N forward. The force of sliding friction is 10 N backward. What is the acceleration of the box? 21. Calculate Mass You push yourself on a skateboard with a force of 30 N east and accelerate at 0.5 m/s2 east. Find the mass of the skateboard if your mass is 58 kg. Assessment 0080_0085_C03S2_894583.indd 85 Online Quiz Section 2 • Newton’s Laws of Motion 85 5/7/10 10:13 AM Section 3 SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. ALSO COVERS: SC.912.N.1.3, MA.912.S.3.2, LA.910.2.2.3 Reading Preview Using Newton’s Laws Essential Questions MAIN Idea Newton’s laws can be used to explain everyday ◗ How does Newton’s first law explain what happens in a car crash? ◗ How does Newton’s second law explain the effects of air resistance? ◗ When is momentum conserved? Review Vocabulary momentum: property of a moving object that equals its mass times its velocity New Vocabulary air resistance terminal velocity free fall centripetal force law of conservation of momentum g Multilingual eGlossary Figure 15 The crash dummies have inertia and resist changes in motion. ■ events, such as falling and collisions. Real-World Reading Link Have you ever stepped off a skateboard and seen the skateboard moved backward? You may have wondered why this happened. Newton’s laws of motion explain this occurrence. What happens in a crash? Newton’s first law of motion can explain what happens in a car crash. When a car traveling about 50 km/h collides head-on with something solid, the car crumples, slows down, and stops within approximately 0.1 s. According to Newton’s first law, the passengers will continue to travel at the same velocity that the car was moving unless a force acts on them. This means that within 0.02 s after the car stops, any unbelted passengers will slam into the windshield, dashboard, steering wheel, or the backs of the front seats, as shown on the left in Figure 15. These unbelted passengers are traveling at the car’s original speed of 50 km/h (about 30 miles per hour). Safety belts Passengers wearing safety belts, also shown in Figure 15, will be slowed down by the force of the safety belt. This prevents the person from being thrown out of the seat. Car-safety experts say that about half of the people who die in car crashes would survive if they wore safety belts. Thousands of others would suffer fewer serious injuries. Even in a low-speed crash, inertia causes the unrestrained dummies to slam into the windshield or seat in front of them. 86 This crash dummy was restrained safely with a safety belt and cushioned with an air bag in this low-speed crash. Chapter 3 • Forces and Newton’s Laws 0086_0092_C03S3_894583.indd 86 5/7/10 10:17 AM The force needed to slow a person’s speed from 50 km/h to 0 in 0.1 s is equal to 14 times the force of gravity on the person. Therefore, safety belts are designed to loosen a little as they restrain the passengers. The loosening increases the time it takes to slow the person down, meaning a smaller acceleration and a smaller force is exerted on the passenger. Air bags Air bags also reduce injuries in car crashes by providing a cushion that reduces the acceleration of the passengers and prevents them from hitting the dashboard. When impact occurs, a chemical reaction occurs in the air bag that produces nitrogen gas. The air bag expands rapidly and then deflates just as quickly as the nitrogen gas escapes out of tiny holes in the bag. The entire process is completed in about 0.04 s. VOCABULARY SCIENCE USAGE V. COMMON USAGE Gravity Science usage an attractive force between any two objects that depends on the masses of the objects and the distance between them Gravity is the force that keeps Earth orbiting around the Sun. Common usage seriousness If you understood the gravity of the situation, you would not find it funny. Newton’s Second Law and Gravitational Acceleration Recall that the gravitational force exerted on an object is equal to the object’s mass times the strength of gravity (Fg = mg). If gravity is the only force acting on an object (Fnet = Fg), then Newton’s second law states that the object’s acceleration is the force of gravity divided by the object’s mass. Notice that the mass cancels and the object’s acceleration due to gravity is equal to the strength of gravity. F Fg Concepts in Motion Animation ■ Figure 16 In a vacuum, there is no air resistance. As a result, the feather and the billiard ball fall with the same acceleration in a vacuum. mg net _ _ a=_ m = m= m =g When discussing the acceleration due to gravity, g is written with the units m/s2. On Earth, any falling object with only gravity acting on it will accelerate at 9.8 m/s2 toward Earth. Air resistance The gravitational force causes objects to fall toward Earth. However, objects falling in the air experience air resistance. Air resistance is a friction-like force that opposes the motion of objects that move through the air. Air resistance acts in the direction opposite to the motion of an object moving through air. If the object is falling downward, air resistance exerts an upward force on the object. The amount of air resistance on an object depends on the size, shape, and speed of the object, as well as the properties of the air. Air resistance, not the object’s mass, is the reason feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and billiard ball. If there were no air resistance, then all objects, including the feather and the billiard ball, would fall with the same acceleration, as shown in Figure 16. Reading Check Explain why some objects fall faster than others. Section 3 • Using Newton’s Laws 0086_0092_C03S3_894583.indd 87 87 5/7/10 10:17 AM Size and shape The more spread out an object is, the more air resistance it will experience. Picture dropping two plastic bags, as shown in Figure 17. One is crumpled into a ball and the other is spread out. When the bags are dropped, the crumpled bag falls faster than the spread-out bag. The downward force of gravity on both bags is the same, but the upward force of air resistance on the crumpled bag is less. As a result, the net downward force on the crumpled bag is greater. Force of gravity Net force Force of gravity Force of air resistance Net force Force of air resistance ■ Figure 17 An object’s surface size and shape determine how fast it will fall. Because of its greater surface area, the bag on the left has more air resistance acting on it as it falls. Concepts in Motion Animation ■ Figure 18 As the sky diver’s speed increases, so does the force of air resistance acting on her. At some point, the force of the air resistance equals the force due to gravity and the sky diver falls at a constant speed called terminal velocity. Fair = 0 N Fnet = 750 N resistance also increases as the object’s speed increases. As an object falls, gravity causes it to accelerate downward. But, as an object falls faster, the upward force of air resistance increases. So, the net force on the object decreases as it falls, as shown with the sky diver in Figure 18. Eventually, the upward air resistance force becomes large enough to balance the downward force of gravity and the net force on the object is zero. Then the acceleration of the object is zero, and the object falls with a constant speed called the terminal velocity. Terminal velocity is the maximum speed an object will reach when falling through a substance, such as air. A falling object’s terminal velocity depends on its size, shape, and mass. For example, the air resistance on an open parachute is much larger than the air resistance on the sky diver alone. With the parachute open, the sky diver’s terminal velocity is small enough that she can land safely. Fair = 375 N Fnet = 375 N Fg = 750 N Sky diver begins to fall. (v is zero) 88 Speed and terminal velocity The amount of air Fair = 750 N F net = 0 N Fg = 750 N Sky diver accelerates downward. (v is increasing) Fg = 750 N Sky diver falls at terminal velocity. (v is constant) Chapter 3 • Forces and Newton’s Laws 0086_0092_C03S3_894583.indd 88 5/7/10 10:24 AM Free fall Suppose an object were falling and there were no air resistance. Gravity would be the only force acting on the object. If gravity is the only force acting on an object, the object is said to be in free fall. For example, the feather and the billiard ball falling in a vacuum, previously shown in Figure 16, are in free fall. Another example is an object in orbit. Earth, for example, is in free fall around the Sun. If Earth did not have a velocity perpendicular to the gravitational force, it would fall into the Sun. Similarly, satellites are in free fall around Earth. Weightlessness You might have seen pictures of astronauts and equipment floating inside an orbiting spacecraft. They are said to be experiencing weightlessness. But, according the law of universal gravitation, the strength of Earth’s gravitational field at a typical orbiting altitude is about 90 percent of its strength at Earth’s surface. So, an 80-kg astronaut would weigh about 700 N in orbit and would not be weightless. What does it mean to say that something is weightless? Think about how you measure your weight. When you stand on a scale, as shown on the left of Figure 19, you are at rest. The net force on you is zero, according to Newton’s second law of motion. The scale exerts an upward force that balances your weight. The dial on a scale shows the size of the upward force, which is the same size as your weight. Now suppose you stand on a scale in an elevator that is in free fall, as on the right in Figure 19. You would no longer push down on the scale at all. The scale dial would read zero, even though the force of gravity has not changed. An orbiting spacecraft is in free fall, and objects in it seem to float because they are all falling around Earth at the same rate. When the elevator is stationary, the scale shows the girl’s weight. Review Additional Practice Problems Concepts in Motion Animation ■ Figure 19 The reading on the scale depends on the upward force the scale exerts on the girl. If both the girl and the scale are in free fall, the girl experiences the sensation of weightlessness, even though the force of gravity has not changed. If the elevator were in free fall, the scale would show a zero weight. M627-10C-MSS02-A Section 3 • Using Newton’s Laws 0086_0092_C03S3_894583.indd 89 89 5/7/10 10:17 AM ■ Figure 20 The riders on this amusement park ride are traveling in a circle because of the centripetal force acting on them. Identify the force that acts as the centripetal force. Centripetal Forces Orbiting objects, such as space shuttles, are traveling in nearly circular paths. According to Newton’s first law, this change in motion is caused by a net force acting on the object. Newton’s second law states that because the object’s acceleration is toward the center of the curved path, the net force is also toward the center. A centripetal force is a force exerted toward the center of a curved path. Anything that moves in a circle is doing so because a centripetal force is accelerating it toward the center. Many different forces can act as a centripetal force. Gravity is the centripetal force that keeps planets orbiting the Sun. On the amusement park ride in Figure 20, the push of the walls of the ride on the people is the centripetal force. When a car rounds a level curve on a highway, friction between the tires and the road acts as the centripetal force. If the road is slippery and the frictional force is small, it might not be large enough to keep the car moving around the curve. Then the car will slide in a straight line, as shown in Figure 21. Force due to friction ■ Figure 21 If the inward frictional force is too small, the car will continue in a straight line and not make it around the curve. 90 Path car would take if there were no friction Chapter 3 • Forces and Newton’s Laws 0086_0092_C03S3_894583.indd 90 5/7/10 10:17 AM p = 1 kg ∙ m/s p = 3 kg ∙ m/s Total momentum = 3 kg ∙ m/s right p = 4 kg ∙ m/s Total momentum = 3 kg ∙ m/s right ■ Force and Momentum Recall that acceleration is the difference between the initial and final velocities, divided by the time. Therefore, we can write Newton’s second law in the following way. (v – v ) Figure 22 When two objects collide and there are no external forces acting on the objects, momentum is conserved. ? Inquiry Virtual Lab (mv – mv ) f i f i =_ F = ma = m × _ t t Recall that an object’s momentum equals its mass multiplied by its velocity. In the equation above, mvf is the final momentum and mvi is the initial momentum. The equation states that the net force exerted on an object equals the change in its momentum divided by the time over which the change occurs. In fact, this is how Newton originally wrote the second law of motion. Conservation of momentum Newton’s second and third laws of motion can be used to describe what happens when objects collide. For example, consider the collision of the balls in Figure 22. We will assume that friction is too small to cause a noticeable change in the balls’ motion. In this ideal case, there are no external forces, but the balls exert forces on each other during the collision. According to Newton’s third law, the forces are equal in size and opposite in direction. Therefore, the momentum lost by the first ball is gained by the second ball and the total momentum of the two balls is the same before and after the collision. This is the law of conservation of momentum—if no external forces act on a group of objects, their total momentum does not change. Review Additional Practice Problems ■ Figure 23 Momentum is conserved in collisions with more than two objects if there are no external forces acting on the objects. The momentum of the cue ball just before the collision is equal to the total of the momentums of the billiard balls (including the cue ball) just after the collision. Collisions with multiple objects When a cue ball hits the group of motionless balls, as shown in Figure 23, the cue ball slows down and the rest of the balls begin to move. The momentum that the group of balls gained is equal to the momentum that the cue ball lost. Momentum is conserved. Section 3 • Using Newton’s Laws 0086_0092_C03S3_894583.indd 91 91 5/7/10 10:17 AM Momentum of rocket Force of rocket on gas Force of gas on rocket Momentum of expelled gases ■ Figure 24 If more gas is ejected from the rocket engine or expelled at a greater velocity, the engine will exert a larger force on the rocket. Section 3 Rocket propulsion Suppose you are standing on skates holding a softball. You exert a force on the softball when you throw it. According to Newton’s third law, the softball exerts a force on you. This force pushes you backward in the direction opposite the softball’s motion. Rockets use the same principle to move, even in the vacuum of outer space. In the rocket engine, burning fuel produces hot gases. The rocket engine exerts a force on these gases and causes them to escape out the back of the rocket. By Newton’s third law, the gases exert a force on the rocket and push it forward. Figure 24 shows one of the Apollo rockets that traveled to the Moon. Notice that the force of the rocket on the gases is equal in size to the force of the gases on the rocket. Momentum is conserved when a rocket ejects the hot gas. If the rocket is initially at rest, then the total momentum of the rocket and the fuel is zero. After the fuel is burned and the hot gas is expelled, the gas travels backward with a momentum of m gasv gas and the rocket travels forward with a momentum of m rocketv rocket. These momentums are equal in size, but opposite in direction. By controlling how much gas is ejected and the gas’s velocity, the rocket’s motion can be controlled. Review Section Summary ◗ In a car crash, an unrestrained passenger will continue moving at the velocity of the car before the crash. ◗ Air resistance is a force that opposes an object’s motion through the air. ◗ If gravity is the only force acting on an object, then the object is in free fall. ◗ Objects appear to be weightless in free fall. ◗ The force that causes an object to move in a circular path is called the centripetal force. ◗ The law of conservation of momentum states that if objects exert forces only on each other, their total momentum is conserved. SC.912.P.12.3 22. MAIN Idea Describe Use Newton’s laws to describe how inertia, gravity, and air resistance affect sky divers as they fall, open their parachutes, and reach terminal velocity. 23. Discuss the advantages of wearing a safety belt when riding in a vehicle. 24. Explain why planets orbit the Sun instead of traveling off into space. 25. Describe what happens to the momentum of two billiard balls that collide. 26. Explain how a rocket can move through outer space where there is no matter for it to push on. 27. Think Critically Suppose you are standing on a scale in an elevator that is accelerating upward. Will the scale read your weight as larger or smaller than the weight it reads when you are stationary? Explain. Apply Math 28. Calculate Momentum A fuel-filled rocket is at rest. It burns its fuel and expels hot gas. The gas has a momentum of 1,500 kg · m/s backward. What is the momentum of the rocket? 92 Chapter 3 • Forces and Newton’s Laws 0086_0092_C03S3_894583.indd 92 Assessment Online Quiz 5/7/10 10:18 AM LAB The Eﬀects of Air Resistance SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. LA.910.2.2.3: The student will organize information to show understanding or relationships among facts, ideas, and events (e.g., representing key points within text through charting, mapping, paraphrasing, summarizing, comparing, contrasting, or outlining). Objectives Effects of Air Resistance n Measure the effect of air resistance on sheets of paper with different shapes. n Design a shape that maximizes air resistance. Use a piece of paper to create your design. Background: If you dropped a bowling ball and a feather from the same height on the Moon, they would both hit the surface at the same time. The objects are attracted to the Moon with the same force, but there is no atmosphere and no air resistance. But on Earth, a bowling ball and a feather will not hit the ground at the same time. Even though all objects on Earth are attracted with the same force, air resistance affects the feather more than it affects the bowling ball. Question: How does air resistance affect the acceleration of falling objects? Preparation Materials paper (4 sheets of equal size) scissors meterstick stopwatch masking tape Safety Precautions Paper Type Time Flat paper Loosely crumpled paper Tightly crumpled paper Your paper design 4. Have one group member drop the flat sheet of paper from the 2.5-m mark. Use the stopwatch to time how long it takes for the paper to reach the ground. Record the time in your data table. 5. Crumple a sheet of paper into a loose ball, and repeat step 4. 6. Crumple a sheet of paper into a tight ball, and repeat step 4. 7. Shape a piece of paper so that it will fall slowly. You may cut, tear, or fold your paper into any design that you choose. Repeat step 4. Conclude and Apply 1. Compare the falling times of the different sheets of paper. 2. Explain why the different-shaped papers fell at different accelerations. 3. Explain how your design caused the force of air resistance on the paper to be greater or smaller than the air resistance on the other paper shapes. Procedure 1. Read the procedure and safety information, and complete the lab form. 2. Copy the data table, or create it on a computer. 3. Measure a height of 2.5 m on the wall, and mark the height with a piece of masking tape. ? Inquiry 0093_0095_C03L1_894583.indd 93 Lab YOUR DATA Compare your paper design with the designs created by your classmates. As a class, compile a list of characteristics that increase air resistance. Chapter 3 • Lab 93 5/3/10 12:06 PM LAB DESIGN YOUR OWN Motion from Diﬀerent Forces SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following: bar graphs, line graphs, stem and leaf plots, circle graphs, histograms, box and whisker plots, scatter plots, and cumulative frequency (ogive) graphs. Goals Make a Plan n Identify several forces that you can use to propel a small toy car across the floor. 1. Read the procedure and safety information, and complete the lab form. 2. As a group, agree upon a hypothesis and decide how you will test it. Identify which results could confirm the hypothesis you have written. 3. Identify the steps that you will need to test your hypothesis. Be sure to include a control run. Be specific. Describe exactly what you will do in each step. Include your materials. 4. Prepare a data table to record your observations. 5. Read the entire experiment to make sure all steps are in logical order and will lead to a useful conclusion. 6. Identify all constants, variables, and controls of the experiment. Make sure your plan tests only one variable at a time. Keep in mind that you will need to measure the toy car’s position at multiple points in time. These points are needed to graph your results. You should have several data points taken after you stop applying the force and before the car starts to slow down. It might be useful to have several students taking measurements, making each responsible for one or two points. n Demonstrate the motion of the toy car using each of the forces. n Graph the position versus time for each force. n Compare the motion of the toy car resulting from each force. Background: Think about a small ball. How many ways could you exert a force on the ball to make it move? You could throw it, kick it, roll it down a ramp, blow it with a large fan, and so on. Question: Do you think the distance and speed of the ball’s motion would be the same for all of these forces? Do you think the acceleration of the ball would be the same for all of these types of forces? Preparation Possible Materials small toy cars ramps or boards of different lengths springs or rubber bands string stopwatch meterstick or tape measure graph paper Safety Precautions Form Make aa Hypothesis Plan Based on your reading and observations, state a hypothesis about how the type of force applied will affect the acceleration, speed, and distance of a toy car. 94 Chapter 3 • Forces and Newton’s Laws 0093_0095_C03L1_894583.indd 94 ? Inquiry Lab 5/13/10 9:47 AM Analyze A nally zeYour Your Plan Data TFollow Test the Model Conclude and Apply Ap pply y 1. Make sure your teacher approves your plan before you begin. 2. Carry out the experiment as planned. 3. While doing the experiment, record your observations in your data table. 1. Evaluate Did the average speed of the toy car vary depending on the force applied to it? 2. Determine For any particular force, did the speed of the toy car change over time? If so, how did the speed change? Describe how you can use your graphs to answer these questions. 3. Draw Conclusions Did your results support your hypothesis? Why or why not? 4. Design Whether or not a hypothesis is supported, experimental results often lead to new hypotheses and experiments. Based on what you have learned from this lab, state a new problem, your hypothesis, and describe how you would test it. Analyze Your Data 1. Graph the position of the car versus time for each type of force that you applied. 2. Analyze How can you use the graphs to compare the speeds of the toy car? 3. Calculate the average speed of the toy car over the same time interval for each type of force that you applied. 4. Analyze How do the calculated average speeds compare? 5. Identify some ways that you might improve your experiment. YOUR DATA Compare your data with those of other students. Discuss how the forces that you applied might be different from those others applied. How were your results affected? Chapter 3 • Lab 0093_0095_C03L1_894583.indd 95 95 5/3/10 12:07 PM Extreme Altitudes SC.912.P.12.3: Interpret and apply Newton’s three laws of motion. SC.912.N.1.3: Recognize that the strength or usefulness of a scientiﬁc claim is evaluated through scientiﬁc argumentation, which depends on critical and logical thinking, and the active consideration of alternative scientiﬁc explanations to explain the data present. n July of 1969, Apollo 11 rocketed toward an historic meeting with the Moon. The editors at The New York Times were in a distinctly uncomfortable position. Forty-nine years before, the newspaper published an editorial that ridiculed the scientist who suggested that rockets could travel in space. Three days before astronauts first walked on the Moon, editors wrote, “The Times regrets the error.” I Rocket man Robert Goddard, shown in Figure 1, was passionate about rocketry. In 1919, Goddard wrote a report to the Smithsonian Institution entitled, “A Method of Reaching Extreme Altitudes.” Near the end of the paper, Goddard proposed that a large rocket propelled by powerful fuel could reach the Moon. Goddard was unprepared for the scornful reaction. Public scorn, private determination An editorial in The New York Times ridiculed Goddard and accused him of lacking “the knowledge ladled out daily in high schools.” According to the writer, even students knew that a rocket could not function in space because there was nothing for the fuel exhaust to push against as it exited the rocket to create forward motion. Goddard continued his experiments, despite the public humiliation. On March 16, 1926, his 3-m rocket, Nell, soared into the sky at 28 m/s. Nell reached a height of 12.5 m, becoming the first liquid-fueled rocket. This launch began the age of modern rocketry that led to space exploration and landing on the Moon. Figure 1 Robert Goddard works on a rocket in 1940. Faulty physics Why was the editorial incorrect? Consider Newton’s third law of motion: For every action, there is an equal and opposite reaction. The writer believed that because the exhaust would have nothing to push against in space, there could be no opposing force pushing the rocket forward. However, he failed to consider what happens inside the rocket. As rocket fuel is burned, a gas is generated. The gas expands rapidly, pushing against everything around it, and escapes through a nozzle at the bottom of the rocket. The escaping exhaust exerts a force on the rocket, causing the rocket to move in the opposite direction. Goddard’s legacy Modern liquid-fueled rockets are based on Goddard’s designs. He developed systems to maintain control of rockets, tested parachute systems to recover spent rockets, put meteorological instruments on rockets to acquire high-altitude weather data, and proposed the idea of multi-stage rockets. Many believe that Goddard’s legacy lies in those first footprints left on the Moon. WebQuest Research Robert Goddard said, “Every vision is a joke until the first man accomplishes it; once realized, it becomes commonplace.” Research a modern technology whose inventors might have been ridiculed had they proposed the idea in 1920. Use your findings to write a brief report. 96 Chapter 3 • Forces and Newton’s Laws 0096_C03HF_894583.indd 96 5/3/10 12:10 PM 3 THEME FOCUS Motion and Forces There are many ways objects interact and exert forces on one another. Friction and air resistance are forces that oppose motion. Gravity is the attractive force between all objects due to mass. BIG Idea A force is a push or pull. Section n 1 Forces MAIN Idea field (p. 77) force (p. 72) friction (p. 74) gravity (p. 76) net force (p. 73) weight (p. 78) • • • • • Unbalanced forces change motion. A force is a push or a pull on an object. The net force on an object is the combination of all the forces acting on the object. Unbalanced forces cause the motion of objects to change. Friction is the force that opposes the sliding motion of two surfaces that are in contact. Gravity is an attractive force between all objects that have mass. Section n 2 Newton’s Laws of Motion inertia (p. 80) Newton’s first law of motion (p. 80) Newton’s second law of motion (p. 82) Newton’s third law of motion (p. 84) MAIN Idea Newton’s laws of motion relate the change in an object’s motion with the forces acting on it. • Newton’s first law of motion states that the motion of an object at rest or moving with constant velocity will not change unless an unbalanced force acts on the object. • Inertia is the tendency of an object to resist a change in motion. • Newton’s second law of motion states that the acceleration of an object depends on its mass and the net force exerted on it. • According to Newton’s third law of motion, when an object exerts a force on a second object, the second object exerts a force on the first object. Section n 3 Using Newton’s Laws air resistance (p. 87) centripetal force (p. 90) free fall (p. 89) law of conservation of momentum (p. 91) terminal velocity (p. 88) Review 0097_C03SG_894583.indd 97 Vocabulary eGames MAIN Idea Newton’s laws can be used to explain everyday events, such as falling and collisions. • In a car crash, an unrestrained passenger will continue moving at the velocity of the car before the crash. • Air resistance is a force that opposes an object’s motion through the air. • If gravity is the only force acting on an object, then the object is in free fall. • Objects appear to be weightless in free fall. • The force that causes an object to move in a circular path is called the centripetal force. • The law of conservation of momentum states that if objects exert forces only on each other, their total momentum is conserved. Chapter 3 • Study Guide 97 5/3/10 12:11 PM 3 SC.912.P.12.2, SC.912.P.12.3, SC.912.P.12.4, MA.912.S.1.2 Use Vocabulary Complete each statement with the correct term from the Study Guide. 29. _________ opposes the sliding motion of two surfaces that are in contact. 30. The _________ of an object is different on every planet in the solar system. 37. Which body exerts the strongest gravita- tional force on you? A) the Moon C) the Sun B) Earth D) this book 38. Which term describes the tendency of an object to resist a change in motion? A) balanced force C) net force B) inertia D) acceleration Use the figure below to answer question 39. 31. When an object moves in a circular path, Speed of a Car the net force is called a(n) _________. that depends on their masses and the distance between them is _________. Speed (m/s) 32. The attractive force between two objects d 30 c 20 10 e b a 33. _________ relates the net force exerted on an object to its mass and acceleration. 0 10 20 30 40 Time (s) Check Concepts 34. What is the gravitational force exerted on an object called? A) centripetal force C) momentum B) friction D) weight 35. Which explains why astronauts seem weightless in orbit? A) Earth’s gravity is much less in orbit. B) The spacecraft is in free fall. C) The gravity of Earth and the Sun cancel. D) The centripetal force on the shuttle balances Earth’s gravity. 36. Which term best describes the forces on an object with a net force of zero? A) balanced forces B) unbalanced forces C) inertia D) acceleration 98 Chapter 3 • Forces and Newton’s Laws 0098_0099_C03CR_894583.indd 98 39. The graph shows the speed of a car moving in a straight line. Over which segments are the forces on the car balanced? A) A and C C) C and E B) B and D D) A, C, and E 40. Which of the following is true about an object in free fall? A) Its acceleration depends on its mass. B) It has no inertia. C) It pulls on Earth, and Earth pulls on it. D) Its momentum is constant. 41. An object always accelerates in the same direction as which of the following? A) net force C) static friction B) air resistance D) gravity 42. BIG Idea Which of the following is not a force? A) weight B) friction C) momentum D) air resistance Assessment Online Test Practice 5/7/10 10:26 AM 3 48. Explain whether there can be forces acting Interpret Graphics on a car that is moving in a straight line with constant speed. 43. Copy and complete the following concept map on forces. 49. Explain You pull open a door. If the force Concepts in Motion Forces Gravity depends on c. d. the door exerts on you is equal to the force you exert on the door, why do you not move? Interactive Concept Map 50. Describe the action and reac- tion force pairs involved when an object falls toward Earth. Ignore the effects of air resistance. a. b. depends on depends on force between surfaces THEME FOCUS surface area e. 51. Explain why a passenger who is not wearing a safety belt will likely hit the windshield in a head-on collision. 52. Determine the direction of the net force on a car if it is slowing down. Explain. Use the table below to answer questions 44–46. Time of Fall for Dropped Objects Object Mass (g) Time of Fall (s) A 5.0 2.0 B 5.0 1.0 C 30.0 0.5 D 35.0 1.5 44. If the objects in the data table above all fell the same distance, which object fell with the greatest average speed? A pply Math 53. Calculate Mass Find your mass if a scale on Earth reads 650 N when you stand on it. 54. Calculate Gravitational Strength You weigh yourself at the top of a high mountain and the scale reads 728 N. If your mass is 75 kg, what is the gravitational strength at your location? Use the figure below to answer question 55. Before Collision 6 kg·m/s 45. Which object was aggeted the most by air resistance? 46. Explain why the four objects do not fall with the same speed. Metal ball After Collision 2 kg·m/s Wooden ball Metal ball p=? Wooden ball 55. Calculate Momentum What is the momen- tum of the wooden ball after the collision? Think Critically 47. Predict Suppose you are standing on a bathroom scale next to a sink. How does the reading on the scale change if you push down on the sink? Explain your prediction. Assessment 0098_0099_C03CR_894583.indd 99 Online Test Practice 56. Calculate Sliding Friction A box being pushed with a force of 85 N right slides along the floor with a constant speed. What is the force of sliding friction on the box? Chapter 3 • Review 99 5/7/10 10:26 AM Standardized Test Practice Multiple Choice Record your answers on the answer sheet provided by your teacher or on a sheet of paper. 5. Which of the following would cause the grav- itational force between object A and object B SC.912.P.12.4 to increase? A. Increase the mass of object A. B. Increase the distance between them. C. Decrease the mass of object A. D. Decrease the mass of both objects. 1. The net force on an object moving with constant speed in circular motion is in which SC.912.P.12.3 direction? A. downward B. opposite to the object’s motion C. toward the center of the circle D. in the direction of the object’s velocity Use the figure below to answer questions 2–4. Object Falling with Air Resistance 25 6. Which of the following is a force? A. friction B. acceleration C. inertia D. velocity Use the figure below to answer question 7. Speed of Sliding Book 1.5 15 Speed (m/s) Speed (m/s) 20 10 5 0 SC.912.P.12.3 0 1 2 3 4 5 Time (s) 1.0 0.5 0 0.5 1.0 1.5 2.0 2.5 Time (s) 2. According to the trend in these data, which of the following values is most likely the speed SC.912.P.12.3 of the object after falling for 6 s? A. 26.7 m/s C. 20.1 m/s B. 15.1 m/s D. 0 m/s 3. Over which of the following time intervals is the acceleration of the object the greatest? SC.912.P.12.3 A. 0 s to 1 s B. 1 s to 2 s C. 2 s to 3 s D. 4 s to 5 s 4. Over which of the following time intervals is the net force on the object the smallest? SC.912.P.12.3 A. 0 s to 1 s C. 2 s to 3 s B. 1 s to 2 s D. 4 s to 5 s 100 Standardized Test Practice 0100_0101_C03STP_894583.indd 100 7. The graph above shows how the speed of a book changes as it slides across a table in a straight line. Over what time interval is the net force on the book in the opposite direcSC.912.P.12.3 tion of the book’s motion? A. 0 s to 0.5 s B. 0.5 s to 2.4 s C. 0 s to 2.4 s D. 2 s to 2.4 s 8. How does the gravitational force change as two objects move farther apart? A. It increases. B. It decreases. C. It remains constant. D. It is zero. Assessment SC.912.P.12.4 Standardized Test Practice 5/3/10 12:09 PM Short Response Extended Response Record your answers on the answer sheet provided by your teacher or on a sheet of paper. Record your answers on a sheet of paper. 13. Give an example of a force applied to an object 9. You are pushing a 30-kg wooden crate across the floor. The force of sliding friction on the crate is 90 N. How much force must you exert on the crate to keep it moving with a SC.912.P.12.3 constant velocity? 10. A sky diver with a mass of 60 kg jumps from an airplane. Five seconds after jumping, the force of air resistance on the sky diver is 300 N. What is the sky diver’s acceleration five seconds after jumping? SC.912.P.12.3 that does not change the object’s velocity. Why does the object’s velocity not change? SC.912.P.12.3 14. A tennis ball is rolling east. You apply a force to it in the north direction. How will your push affect the direction of the ball? Explain. SC.912.P.12.3 15. Two balls are dropped from an airplane. Both balls are the same size, but one has a mass ten times greater than the other. The force of air resistance on each ball depends on the ball’s speed. Explain whether both balls will reach the same terminal velocity. 11. A pickup truck is carrying a load of gravel. SC.912.P.12.3 The driver hits a bump and gravel falls out, so that the mass of the truck is one half as large after hitting the bump. If the net force on the truck does not change, how does the truck’s acceleration change? SC.912.P.12.3 Use the table below to answer question 12. 16. When the space shuttle is launched from Earth, the rocket engines burn fuel and apply a constant force on the shuttle until they burn out. Explain why the shuttle’s acceleration increases while the rocket SC.912.P.12.3 engines are burning fuel. 17. An object in motion slows down and comes Car Mass (kg) Stopping Distance (m) A B 1,000 1,250 80 100 C D 1,500 2,000 120 160 to a stop. Use Newton’s first law of motion to explain why this happens. SC.912.P.12.3 18. In an airplane flying at a constant speed, the force pushing the airplane forward is exerted by the engine and is equal to the opposite force of air resistance. Describe how these forces compare when the plane speeds up and slows down. In which direction is the net force on the airplane in each case? 12. What is the relationship between a car’s mass and its stopping distance? How can SC.912.P.12.3 you explain this relationship? SC.912.P.12.3 NEED EXTRA HELP? If You Missed Question . . . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Review Section . . . 3 3 3 3 1 1 2 1 2 3 2 2 1 2 3 2 2 2 Assessment 0100_0101_C03STP_894583.indd 101 Standardized Test Practice Standardized Test Practice 101 5/3/10 12:09 PM