Momentum & Impulse 1 Check Your Understanding (to be completed on a separate sheet of paper) Express your understanding of the concept and mathematics of momentum by answering the following questions. 1. Explain why it is difficult for a firefighter to hold a hose which ejects large amounts of high-speed water. 2. A large truck and a Volkswagen have a head-on collision. a. Which vehicle experiences the greatest force of impact? b. Which vehicle experiences the greatest impulse? c. Which vehicle experiences the greatest momentum change? d. Which vehicle experiences the greatest acceleration? 3. Miles Tugo and Ben Travlun are riding in a bus at highway speed on a nice summer day when an unlucky bug splatters onto the windshield. Miles and Ben begin discussing the physics of the situation. Miles suggests that the momentum change of the bug is much greater than that of the bus. After all, argues Miles, there was no noticeable change in the speed of the bus compared to the obvious change in the speed of the bug. Ben disagrees entirely, arguing that that both bug and bus encounter the same force, momentum change, and impulse. Who do you agree with? Support your answer. 2 4. If a ball is projected upward from the ground with ten units of momentum, what is the momentum of recoil of the Earth? ____________ Do we feel this? Explain. 5. If a 5-kg bowling ball is projected upward with a velocity of 2.0 m/s, then what is the recoil velocity of the Earth (mass = 6.0 x 10^24 kg). 6. A 120 kg lineman moving west at 2 m/s tackles an 80 kg football fullback moving east at 8 m/s. After the collision, both players move east at 2 m/s. Draw a vector diagram in which the before- and after-collision momenta of each player is represented by a momentum vector. Label the magnitude of each momentum vector. Before After 7. Would you care to fire a rifle that has a bullet ten times as massive as the rifle? Explain. 8. A baseball player holds a bat loosely and bunts a ball. Express your understanding of momentum conservation by filling in the tables below. 3 9. A Tomahawk cruise missile is launched from the barrel of a mobile missile launcher. Neglect friction. Express your understanding of momentum conservation by filling in the tables below. Isolated System Notes Total system momentum is conserved for collisions occurring in isolated systems. But what makes a system of objects an isolated system? And is momentum conserved if the system is not isolated? This is the focus of this part of Lesson 2. A system is a collection of two or more objects. An isolated system is a system which is free from the influence of a net external force. There are two criteria for the presence of a net external force; it must be... a force which originates from a source other than the two objects of the system a force that is not balanced by other forces. 4 Check Your Understanding I Concepts of Physics - Mr. Kuffer Express your understanding of the concept and mathematics of momentum by answering the following questions. 1. Determine the momentum of a ... a. 60-kg halfback moving eastward at 9 m/s. b. 1000-kg car moving northward at 20 m/s. c. 40-kg freshman moving southward at 2 m/s. 2. A car possesses 20 000 units of momentum. What would be the car's new momentum if ... a. its velocity were doubled. b. its velocity were tripled. c. its mass were doubled (by adding more passengers and a greater load) d. both its velocity were doubled and its mass were doubled. 3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are running down the football field. Consider their ticker tape patterns below. Compare the velocities of these three players. How many times greater is the velocity of the halfback and the velocity of the tight end than the velocity of the lineman? Which player has the greatest momentum? Explain. 5 Vector Diagram Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? ________________________________________________________________________ Velocity-Time Graph Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? ________________________________________________________________________ Ticker Tape Diagram Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? 6 Check Your Understanding Part II Concepts of Physics - Mr. Kuffer Express your understanding of the impulse-momentum change theorem by answering the following questions. 1. A 0.50-kg cart (#1) is pulled with a 1.0-N force for 1 second; another 0.50 kg cart (#2) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #2) has the greatest acceleration? Explain. Which cart (#1 or #2) has the greatest impulse? Explain. Which cart (#1 or #2) has the greatest change in momentum? Explain. 2. In a phun physics demo, two identical balloons (A and B) are propelled across the room on horizontal guide wires. The motion diagrams (depicting the relative position of the balloons at time intervals of 0.05 seconds) for these two balloons are shown below. Which balloon (A or B) has the greatest acceleration? Explain. 7 Which balloon (A or B) has the greatest final velocity? Explain. Which balloon (A or B) has the greatest momentum change? Explain. Which balloon (A or B) experiences the greatest impulse? Explain. 3. Two cars of equal mass are traveling down Lake Avenue with equal velocities. They both come to a stop over different lengths of time. The ticker tape patterns for each car are shown on the diagram below. At what approximate location on the diagram (in terms of dots) does each car begin to experience the impulse. Which car (A or B) experiences the greatest acceleration? Explain. 8 Which car (A or B) experiences the greatest change in momentum? Explain. Which car (A or B) experiences the greatest impulse? Explain. 4. The diagram to the right depicts the before- and after-collision speeds of a car which undergoes a head-on-collision with a wall. In Case A, the car bounces off the wall. In Case B, the car "sticks" to the wall. In which case (A or B) is the change in velocity the greatest? Explain. In which case (A or B) is the change in momentum the greatest? Explain. In which case (A or B) is the impulse the greatest? Explain. In which case (A or B) is the force which acts upon the car the greatest (assume contact times are the same in both cases)? Explain. 9 5. Rhonda, who has a mass of 60.0 kg, is riding at 25.0 m/s in her sports car when she must suddenly slam on the brakes to avoid hitting a dog crossing the road. She strikes the air bag, which brings her body to a stop in 0.400 s. What average force does the seat belt exert on her? If Rhonda had not been wearing her seat belt and not had an air bag, then the windshield would have stopped her head in 0.001 s. What average force would the windshield have exerted on her? 6. A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck. 7. If a 5-kg object experiences a 10-N force for a duration of 0.1-second, then what is the momentum change of the object? 10 Check Your Understanding Part III Concepts of Physics - Mr. Kuffer Express your understanding of Newton's third law by answering the following questions. 1. While driving down the road, an unfortunate bug strikes the windshield of a bus. Quite obviously, a case of Newton's third law of motion. The bug hit the bus and the bus hit the bug. Which of the two forces is greater: the force on the bug or the force on the bus? 2. Rockets are unable to accelerate in space because ... a. there is no air in space for the rockets to push off of. b. there is no gravity is in space. c. there is no air resistance in space. d. ... nonsense! Rockets do accelerate in space. 3. A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards. The acceleration of the recoiling gun is ... a. greater than the acceleration of the bullet. b. smaller than the acceleration of the bullet. c. the same size as the acceleration of the bullet. 11 4. Would it be a good idea to jump from a rowboat to a dock that seems within jumping distance? Explain. 5. If we throw a ball horizontally while standing on roller skates, we roll backward with a momentum that matches that of the ball. Will we roll backward if we go through the motion of throwing the ball without letting go of it? Explain. 6. Suppose there are three astronauts outside a spaceship and two of them decide to play catch with the other woman. All three astronauts weigh the same on Earth and are equally strong. The first astronaut throws the second astronaut towards the third astronaut and the game begins. Describe the motion of these women as the game proceeds. Assume each toss results from the same-sized "push." How long will the game last? 12 Egg Drop Lab Theory and Inquiry I. Explain the theory behind the egg drop lab impulse = Ft = mv = Explain where the equation above came from and how it helps in constructing the egg drop apparatus. II. Choose an equation from your equation sheet that will allow you to solve for the final velocity of your egg. Calculate the final velocity of your egg. You have to measure a variable in order to solve for the final velocity. What is the variable? Scoring: 1. Complete all questions in lab notebook 2. Egg drop apparatus is constructed 3. Egg survives drop from 1st flight of bleachers 4. Egg survives drop from top of bleachers Total: 10 pts 5 pts 5 pts +5 pts 20 pts must be able to easily place and remove egg in apparatus may only use cardboard, drinking straws, paper, and non-padded tape may not use any parachute apparatus apparatus may not exceed an 8 inch cube or sphere in size 13 14 15 Hewitt Post-Video 1. Why does a boxer move his/her head away from the blow? Explain. 2. Cart 1 approaches cart 2 with a momentum of 10 units. If cart 2 is initially at rest what is the momentum before the collision? a. If the carts stick together, what is their momentum after the collision? b. Compared to cart 1’s velocity before the collision, what must their velocity be after the collision? (assume the carts are of equal mass) c. Draw the before and after situation below. before: after: d. What law of physics does this support? e. Write the equation for this law. Bonus: _________ provides more impulse than hitting. 16 Momentum Video quiz (ESPN) Name_______________ Date_______ Period____ 1. What is “sick” about momentum? ___________________________ 2. What common force effects momentum? ________________ 3. What happens to the momentum of objects that stick together? _______________________________________________ 4. What happens to the velocity of objects that stick together? _______________________________________________ 5. If two objects have the same mass with velocities in opposite directions, what happens when they collide? _______________________ 6. Based on physical evidence, did the driver stop at the stop sign? ____ Impulse Video Quiz w/ Napolean Kauffman (ESPN) Name:_______________ Date:________ 1. Napolean Kauffman does what when he gets hit by other football players? ______________________________ 2. ______________ is what makes force an impulse. 3. One watermelon broke. One did not. Why?________________________________________________ ____________________________________________________ ____________________________________________________ 4. In sports, whether throwing, kicking, or hitting the ball, you are told to “follow through”. Why is your “follow through” so important? ____________________________________________________ ____________________________________________________ 17 Momentum Lab Preliminary Questions: 1. Momentum is “__________________________________________” 2. List three examples of objects with a large amount of momentum Instructions: 1. Set up the lab as indicated (and shown below) 2. Set the carts into motion by activating the spring mechanism 3. Calculate their momenta at the two points on the track. 4. IN YOUR LAB NOTEBOOK… fill in all of the data table 5. REMEMBER… Trials 6-9 are done on a slightly inclined track Photogates Flag Calculations: Since you cut a flag for the cart that is 2.54 cm (0.0254 m) wide, the velocity of the cart can be calculated in the following manner… V = ∆d/t * Where ∆d is 0.0254 m and the time is given by the photogate Analysis Questions: 1. The momentum should not be the same at both positions… Why? 2. What would you find if a third photogate was placed along the track? 18 Data at Position #1 Trial # Horizontal track Incline in track Mass of Cart (kg) Extra mass (kg) Total Mass (kg) Time at Position #1 (s) Velocity at Position #1 (m/s) Momentum at Position #1 (kg m/s) 1 2 3 4 5 6 7 8 9 Data at Position #2 Trial # Horizontal track Incline in track Time at Position #2 (s) Velocity at Position #2 (m/s) Momentum at Position #2 (kg m/s) “Lost” / Gained Momentum (kg m/s) 1 2 3 4 5 6 7 8 9 19 Explosion Lab Investigating the Law of Conservation of Momentum NAME:_____________________ m1V1 + m2V2 = m1V1' + m2V2' Cart #1 (Cart moving to the left after explosion) Trial # Mass of Cart (kg) 1 2 3 4 5 6 7 8 9 .5 .5 .5 .5 .5 .5 .5 .5 .5 Additional Mass in Cart (kg) 0 .1 .2 .3 .4 .5 .6 .7 .8 Total Mass (kg) Time Velocity Momentum (s) (m/s) (kg m/s) Cart #2 (Cart moving to the right after explosion) Trial # 1 2 3 4 5 6 7 8 9 Mass of Cart (kg) .5 .5 .5 .5 .5 .5 .5 .5 .5 Additional Mass in Cart (kg) Total Mass (kg) Time Velocity Momentum Difference in (s) (m/s) (kg m/s) Momentum of Two Carts (kg m/s) 0 0 .1 .2 .3 .4 .5 .6 .7 * Was there a difference in the momentum of the two carts? If there was, why? If there wasn’t, why not? 20 Momentum and Collisions The collision of two carts on a track can be described in terms of momentum conservation. If there is no net external force experienced by the system of two carts, then we expect the total momentum of the system to be conserved. This is true regardless of the force acting between the carts. Collisions are classified as elastic (kinetic energy is conserved), inelastic (kinetic energy is lost) or completely inelastic (the objects stick together after collision). In this experiment you can observe most of these types of collisions and test for the conservation of momentum and energy in each case. OBJECTIVES Observe collisions between two carts, testing for the conservation of momentum. Classify collisions as elastic, inelastic, or partially elastic. MATERIALS computers Vernier computer interface Logger Pro two Vernier Motion Detectors dynamics cart track two low-friction dynamics carts with magnetic and Velcro™ bumpers PRELIMINARY QUESTIONS 1. Consider a head-on collision between two billiard balls. One is initially at rest and the other moves toward it. Sketch a position vs. time graph for each ball, starting with time before the collision and ending a short time afterward. 2. As you have drawn the graph, is momentum conserved in this collision? PROCEDURE 1. Measure the masses of your carts and record them in your data table. Label the carts as cart 1 and cart 2. 2. Set up the track so that it is horizontal. Test this by releasing a cart on the track from rest. The cart should not move. 3. Practice creating gentle collisions by placing cart 2 at rest in the middle of the track, and release cart 1 so it rolls toward the first cart, magnetic bumper toward magnetic bumper. The carts should smoothly repel one another without physically touching. 4. Place a Motion Detector at each end of the track, allowing for the 0.4 m minimum distance between detector and cart. Connect the Motion Detectors to the DIG/SONIC 1 and DIG/SONIC 2 channels of the interface. 5. Open the file “19 Momentum Coll” from the Physics with Computers folder. 21 6. Click to begin taking data. Repeat the collision you practiced above and use the position graphs to verify that the Motion Detectors can track each cart properly throughout the entire range of motion. You may need to adjust the position of one or both of the Motion Detectors. 7. Place the two carts at rest in the middle of the track, with their Velcro bumpers toward one another and in contact. Keep your hands clear of the carts and click . Select both sensors and click . This procedure will establish the same coordinate system for both Motion Detectors. Verify that the zeroing was successful by clicking and allowing the still-linked carts to roll slowly across the track. The graphs for each Motion Detector should be nearly the same. If not, repeat the zeroing process. Part I: Magnetic Bumpers 8. Reposition the carts so the magnetic bumpers are facing one another. Click to begin taking data and repeat the collision you practiced in Step 3. Make sure you keep your hands out of the way of the Motion Detectors after you push the cart. 9. From the velocity graphs you can determine an average velocity before and after the collision for each cart. To measure the average velocity during a time interval, drag the cursor across the interval. Click the Statistics button to read the average value. Measure the average velocity for each cart, before and after collision, and enter the four values in the data table. Delete the statistics box. 10. Repeat Step 9 as a second run with the magnetic bumpers, recording the velocities in the data table. Part II: Velcro Bumpers 11. Change the collision by turning the carts so the Velcro bumpers face one another. The carts should stick together after collision. Practice making the new collision, again starting with cart 2 at rest. 12. Click to begin taking data and repeat the new collision. Using the procedure in Step 9, measure and record the cart velocities in your data table. 13. Repeat the previous step as a second run with the Velcro bumpers. Part III: Velcro to Magnetic Bumpers 14. Face the Velcro bumper on one cart to the magnetic bumper on the other. The carts will not stick, but they will not smoothly bounce apart either. Practice this collision, again starting with cart 2 at rest. 15. Click to begin data collection and repeat the new collision. Using the procedure in Step 9, measure and record the cart velocities in your data table. 16. Repeat the previous step as a second run with the Velcro to magnetic bumpers. 22 DATA TABLE Mass of cart 1 (kg) Run number Run number Mass of cart 2 (kg) Velocity of cart 1 before collision Velocity of cart 2 before collision Velocity of cart 1 after collision Velocity of cart 2 after collision (m/s) (m/s) (m/s) (m/s) 1 0 2 0 3 0 4 0 5 0 6 0 Momentum of cart 1 before collision (kg•m/s) Momentum of cart 2 before collision (kg•m/s) 1 0 2 0 3 0 4 0 5 0 6 0 Momentum of cart 1 after collision (kg•m/s) 90% ELASTIC proton colliding with another proton Total momentum before collision (kg•m/s) Total momentum after collision (kg•m/s) Ratio of total momentum after/before under-inflated basketball bouncing billiard balls colliding 100% Momentum of cart 2 after collision (kg•m/s) 30% inflated basketball bouncing 0% INELASTIC In this lab, we will collide two collision carts together to determine if momentum is conserved in all types of collisions. To do this, we will obviously need to measure the velocity and mass of each cart both before and after the collision. The above diagram might help you keep things straight. 23 ANALYSIS 1. Determine the momentum (mv) of each cart before the collision, after the collision, and the total momentum before and after the collision. Calculate the ratio of the total momentum after the collision to the total momentum before the collision. Enter the values in your data table. 2. If the total momentum for a system is the same before and after the collision, we say that momentum is conserved. If momentum were conserved, what would be the ratio of the total momentum after the collision to the total momentum before the collision? 3. For your six runs, inspect the momentum ratios. Even if momentum is conserved for a given collision, the measured values may not be exactly the same before and after due to measurement uncertainty. The ratio should be close to one, however. Is momentum conserved in your collisions? 4. Classify the three collision types as elastic, inelastic, or completely inelastic. EXTENSIONS 1. Using a collision cart with a spring plunger, create a super-elastic collision; that is, a collision where kinetic energy increases. The plunger spring should be compressed and locked before the collision, but then released during the collision. Measure momentum before and after the collision. Is momentum conserved in this case? 2. Using the magnetic bumpers, consider other combinations of cart mass by adding weight to one cart. Is momentum conserved in these collisions? 3. Using the magnetic bumpers, consider other combinations of initial velocities. Begin with having both carts moving toward one another initially. Is momentum conserved in these collisions? * Answer on a separate sheet of paper!!! 24 Physics of ‘the Hit’ Julie Jacobson/Associated Press Baltimore running back Willis McGahee was knocked unconscious after a collision with the Steelers' Ryan Clark in the A.F.C. championship game. Published: January 30, 2009 TAMPA, Fla. — Isaac Newton’s apple hurt considerably less than Ryan Clark’s coconut. But they did have a few things in common. Clark’s shockingly violent hit on the Baltimore Ravens’ Willis McGahee two Sundays ago — a fullspeed, helmet-to-helmet crash that left McGahee unconscious and Clark all but — didn’t just follow the N.F.L.’s rules, but Newton’s as well. Force equaled mass times acceleration. Momentum was conserved. And the bodies finally came to rest, McGahee’s on a stretcher. A head-on hit from the Jets’ Eric Smith sent the Cardinals’ Anquan Boldin to the hospital. “How I look at it, you can be the hammer or the nail,” the inner scientist in Clark explained this week. “I try to be the hammer.” The tackle, the art of making the ball carrier not stay in motion, is football’s most primeval action. Amusing physicists the way batting averages do actuaries, collisions 25 lead the highlight reels, impart the force of a deadly car crash, and rely upon kinematics that date to a considerably different big bang. Sunday’s Super Bowl could very well ride on how well the Steelers’ defense — known as perhaps the most fearsome and bone-clattering in the N.F.L. — can tackle the Arizona Cardinals’ fast and evasive wide receivers. From angles and acceleration to speed and centers of gravity, players might not understand the physics of tackling, but they know how to wield it. “It’s all about timing and leverage,” Cardinals safety Adrian Wilson said. “Being able to time the hit the right way, and the leverage you’ve got to have once you make impact so the other player goes back, and not you.” Trying to trip up or throw down a ball carrier with only one’s arms can be a risky maneuver. Barreling straight into him with 200-plus pounds of muscle at 20 miles an hour is a more reliable impediment. From there, Newton’s second law of motion (force equals mass times acceleration) and conservation of momentum take over. Mass is the players’ weight, which in the N.F.L. grows higher every decade. Acceleration is not that of the incoming tackler, as is often assumed, but how quickly both the defender and runner slow down through impact. It is this duration of impact, between one- and two-tenths of a second by many estimates, that has tremendous effect on the force of a football collision. Hard objects repel each other quickly; equally heavy but softer objects have “give” that allows their contact to last longer and accept the force less jarringly. It’s the difference between being hit by a baseball and being hit by an overripe peach. “The tackler doesn’t want his body to be a big spring — these players lower their shoulder and tense up and launch to make their force go up,” said Stefan Duma, a professor of mechanical engineering at Virginia Tech who has studied the similarities between football collisions and car crashes. “It’s like trying to break down a door — you try to get all your mass behind you and drive it through one point. You want to get all your mass to act as one mass, one missile.” Reaching the ball carrier at full speed is crucial, as any deceleration before impact saps force from the hit. This is where angles come in, said Timothy Gay, a professor of 26 physics at the University of Nebraska-Lincoln and the author of “Football Physics: The Science of the Game.” Football instincts allow the best safeties to anticipate where the runner or receiver will be and then take the shortest route to him, maintaining speed and even allowing for one final push. “Jack Tatum was vicious — that helps — but he had a way of popping with the perfect angle and timing,” Gay said of the former Oakland Raiders safety called the Assassin in both reverence and fear. “The best hitters accelerate at the last instant. That final jolt of speed allows them to apply a bigger force to their victim.” Ask a physicist and a coach where that force should be applied, and they can answer differently. Gay said that the hit should be applied at the runner’s center of mass — just below the rib cage in the center of the chest — to direct all the force into stopping his forward motion. Missing that spot by too much, Gay said, “Causes the ball carrier to rotate around his center of mass, and he might not go down. The announcer would say, ‘He bounced off him.’ ” But Ray Horton, the Steelers’ defensive backs coach, preaches a different approach. He is all for the ball carrier rotating, as long as he does so violently enough to wind up on the turf. “We teach you tackle at the knees — if you tackle at the thigh to the shoulders, that’s his power box,” Horton said. “If I want something to tip over, I don’t want to hit it in its center of gravity, because it might go straight back and stay upright. If I want it to go down, I want to hit below the center of gravity, and that’s why we hit by the knees.” Horton added: “Low man wins. If you hit him too high, he’s going to run you over because of the physics of how big these guys are.” Which is why trying to run over the most massive running backs, from Earl Campbell to Brandon Jacobs, is asking for your action to get an equal and opposite (not to mention embarrassing) reaction, with you on the ground and the runner continuing onward. Because momentum — defined as mass times velocity — is conserved in all collisions, Jacobs moving at any decent speed is almost impossible to stop by an outweighed defender’s merely running into him. Tripping him or wrapping him up and waiting for help is a far better option, as long as you are not under him when he finally falls. Running backs do not sustain the hardest shots in football, though. Few plays get more oohs and 27 aahs than when a lithe receiver crosses the middle and, with or without the ball, gets hit squarely by an oncoming safety. Duma suggested imagining the body as a primary mass (the torso) in the middle with several other masses connected by springs (the limbs and neck) attached to it. When the tense and intent defender hits the center of this object, the torso accelerates back while the head and feet stay behind temporarily, before flopping back. These are the hits that make the highlights. Duma said that in his experience — he watches dozens of N.F.L. games each season — these hits are more frequent at the end of games already in hand. “When you’re up, your defense hits harder,” Duma said. “They take more risks. If you come across the middle on the slant, they’re going to go after you and not worry about missing the tackle and giving up the touchdown.” He added: “I think that’s what you saw on the Clark-McGahee hit at the end of the last game. I saw it a lot in these playoffs. Baltimore against the Dolphins, they were just leveling people. Ed Reed could run all over the backfield, and if he was out of position, they wouldn’t lose the game.” Clark appeared to concur. On Wednesday, he said: “The McGahee hit, that was a point where I probably could have stopped and waited and tried to tackle him, but it’s sad to say I think I closed my eyes and I was praying that I’d wake up when I hit the ground.” In the end, players leave physics out of their own definitions of hard hits. Anquan Boldin, the Cardinals’ receiver who was hit so high and hard by a Jets defender earlier this season that he now has 7 plates and 40 screws in his face, said he defined the perfect hit as “when you get hit hard enough to make you rethink about having anything to do with the ball,” which apparently the Jets hit still was not. Clark said, “What makes a good hit is not getting fined.” Clark said he was not particularly familiar with Newton’s laws — but then offered his own theory of momentum, one he plans to use in Sunday’s Super Bowl. 28 “A good hit can change the momentum of the game,” he said. “If we come out there and hit them, be physical with them, and get a good hit early, I think they might go back to the quarterback and say, ‘How ’bout you not throw the ball in there?’ ” January 31, 2009 29