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Concepts of Physics Mr. Kuffer 1 Mr. Küffer’s Guide to Problem Solving… Just Guesss! Given - Identify given information Unknown - Identify unknown information… What is the problem asking you to solve? Equation - Select the appropriate equation Substitute - Substitute the given information into the equation Solve - Solve the problem! Stupid Step - Put a square around your final answer to separate it from the rest of your work, double check your units, and ask yourself… Does the answer I got seem reasonable? 2 Purpose: To create graphs in order to estimate and predict values (mass). Procedure: 1. Measure the length of three wires to the smallest increment of your measurement tool (ruler). 2. Measure the mass of only the longest and shortest wires. 3. Make a graph of mass (vertical) versus length (horizontal). Include units on the graph. 4. Use the graph to predict the mass of the middle wire. Observations and Data: 1. Does your graph of wire mass versus length pass through the origin? 2. Should it? Why or why not? 3. Calculate the slope of the graph, including the units. 4. Explain the significance of determining the slope (a.k.a. What does the slope tell us?) Applications: 1. In the pharmaceutical industry, how might the weight of the compressed tablets be used to determine the quantity of finished tablets produced in a specific lot? 3 Concepts of Physics Mr. Kuffer Graphical Analysis with Excel (Refer to Visualizing Data Packet as a supplemental) 1) 2) What are the two (main) types of relationships that we will discuss this year in Concepts of Physics? During an experiment, a student measured the mass of 10.0 cm3 of alcohol. The student then measured the mass of 20.0 cm3 of alcohol. In this way the data in the table below was collected. a. Plot a graph of the data, including a best-fit line. b. Describe the resulting curve. c. Use the graph to write a three variable equation for the volume to the mass of alcohol. d. Find the units of the slope of the graph. What is the name given to this quantity? e. What would the mass of 35 cm3 of alcohol be? (interpolate, step 17) f. A mass for 60 cm3 of alcohol be? (extrapolate, step 23) Volume (cm3) 10 20 30 40 50 Mass (g) 7.9 15.8 23.7 31.6 39.6 FYI: VOCAB: 1. DEPENDENT VARIABLE – the variable that may change as a result of changes purposely made in independent variable. (Plotted on the vertical axis) 2. INDEPENDENT VARIABLE (manipulated variable) – the variable that is changed on purpose by the experimenter. (Plotted on the horizontal axis) 4 3) During a class demonstration, Mr. Kuffer placed a 1.0 kg mass on a horizontal table that was nearly frictionless. Mr. Kuffer then applied various horizontal forces to the mass and measured the rate at which it gained speed (was accelerated) from each force applied. The results of the experiment are shown below. a. Plot a graph of the data, including a best-fit line. b. Describe the relationship between force and acceleration according to the graph. c. Use the graph to write an equation relating force and acceleration (Hint: Newton’s 2nd Law… F = ma). d. Find the units of the slope of the graph. Acceleration (m/s2) 4.9 9.8 15.2 20.1 25.0 29.9 4) Force (N) 5 10 15 20 25 30 This time Mr. Kuffer changes the procedure a bit. The mass was varied while the force was kept constant. The acceleration of each mass was recorded. The results of the experiment are shown below. a. Plot a graph of the data, including a best-fit line for the curve. b. Describe the resulting curve. c. According to the graph, what is the relationship between mass and the acceleration produced by a constant force? d. Find the units of the slope of the graph. Mass (kg) 1 2 3 4 5 6 Acceleration (m/s2) 12.0 5.9 4.1 3.0 2.5 2.0 5 6 7 8 9 Graphical Analysis Rules: What does it all mean? Identify the graph Identify the slope (+ / -) Is the line straight? Must be constant Is the line curved? Must be changing Is it increasing or decreasing? Using the rules above, write a complete description of the motion indicated by each graph below. (SEPARATE SHEET OF PAPER) A B d C d D d d t t F d t t G d t H d d t E t t 10 Visualizing Data Lab Ticker Timer w/ Power Point Objective: • • • Graph the relationship between dependent and independent variables Recognize linear and direct relationships Interpret the slope of a curve Recognize quadratic and inverse relationships Procedure: • • • • • • • • • • Set up track on level surface (lab table) tape ticker timer to dynamics cart track run strip of paper through ticker time (be sure the timer is off) tape paper to dynamics cart turn ticker time to “on” position gently push dynamics cart away from timer Plot distance vs time graph – every six data points equals one tenth of a second label graphs accordingly draw a best fit line through the points interpret line 11 HW #1 Plotting Line Graphs 1. Identify the independent and dependent variables in your data. The independent variable is plotted on the horizontal axis, or x-axis. The dependent variable is plotted on the vertical axis, or y-axis. 2. Determine the range of the independent variable to be plotted. 3. Decide whether the origin (0,0) is a valid data point 4. Spread the data out as much as possible. Let each division on the graph paper stand for a convenient unit. 5. Number and label the horizontal axis. 6. Repeat steps 2-5 for the dependent variable. 7. Plot the data points on the graph. 8. Draw a “best-fit” straight line or smooth curve that passes through as many data points as possible. Do not use a series of straight line segments that “connect the dots” 9. Give the graph a title that clearly tells what the graph represents. Graph the Following Graph on Excel! Data Set #1 distance (m) 1 2 3 4 5 6 7 8 9 Data Set # 2 time (s) 1 4 9 16 25 36 49 64 81 speed (m/s) 10 20 30 40 50 60 70 80 90 time (s) 2 4 6 8 10 12 14 16 18 HW w/ Hewitt Overheads! 12 Graph Matching One of the most effective methods of describing motion is to plot graphs of position, velocity, and acceleration vs. time. From such a graphical representation, it is possible to determine in what direction an object is going, how fast it is moving, how far it traveled, and whether it is speeding up or slowing down. In this experiment, you will use a Motion Detector to determine this information by plotting a real time graph of your motion as you move across the classroom. The Motion Detector measures the time it takes for a high frequency sound pulse to travel from the detector to an object and back. Using this round-trip time and the speed of sound, you can determine the position to the object. Logger Pro will perform this calculation for you. It can then use the change in position to calculate the object’s velocity and acceleration. All of this information can be displayed either as a table or a graph. A qualitative analysis of the graphs of your motion will help you develop an understanding of the concepts of kinematics. walk back and forth in front of Motion Detector OBJECTIVES Analyze the motion of a student walking across the room. Predict, DESCRIBE, sketch, and test position vs. time kinematics graphs. Predict, DESCRIBE, sketch, and test velocity vs. time kinematics graphs. MATERIALS computer Vernier computer interface Logger Pro Vernier Motion Detector meter stick masking tape 13 PRELIMINARY QUESTIONS 1. Use a coordinate system with the origin at far left and positive positions increasing to the right. Sketch the position vs. time graph for each of the following situations: a) b) c) d) An object at rest An object moving in the positive direction with a constant speed An object moving in the negative direction with a constant speed An object that is gradually accelerating in the positive direction, starting from rest 2. Sketch the velocity vs. time graph for each of the situations described above. PROCEDURE Part l Preliminary Experiments 1. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. 2. Place the Motion Detector so that it points toward an open space at least 4 m long. Use short strips of masking tape on the floor to mark the 1 m, 2 m, 3 m, and 4 m positions from the Motion Detector. 3. Open the file “01a Graph Matching” from the Physics with Computers folder. 4. Using Logger Pro, produce a graph of your motion when you walk away from the detector with constant velocity. To do this, stand about 1 m from the Motion Detector and have your lab partner click . Walk slowly away from the Motion Detector when you hear it begin to click. 5. Sketch what the position vs. time graph will look like if you walk faster. Check your prediction with the Motion Detector. 6. Try to match the shape of the position vs. time graphs that you sketched in the Preliminary Questions section by walking in front of the Motion Detector. Part Il Position vs. Time Graph Matching 7. Open the experiment file “01b Graph Matching.” A position vs. time graph will appear. 8. Write a complete description of how you would walk to produce this target graph. Do this in your lab notebook. 9. To test your prediction, choose a starting position and stand at that point. Start data collection by clicking . When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the computer screen. 10. If you were not successful, repeat the process until your motion closely matches the graph on the screen. Sketch your graph, including all significant data points. 11. Open the experiment file “01c Graph Matching” and repeat Steps 8 – 10, using a new target graph. 12. Answer the Analysis questions for Part II before proceeding to Part III. 14 Part IIl Velocity vs. Time Graph Matching 13. Open the experiment file “01d Graph Matching.” A velocity vs. time graph will appear. 14. Describe how you would walk to produce this target graph. (written explanation should be included in your lab notebook) 15. To test your prediction, choose a starting position and stand at that point. Start by clicking . When you hear the Motion Detector begin to click, walk in such a way that the graph of your motion matches the target graph on the screen. It will be more difficult to match the velocity graph than it was for the position graph. 16. Open the experiment file “01e Graph Matching.” Repeat Steps 14 – 15 to match this graph. (Again sketch your graph) 17. Remove the masking tape strips from the floor. ANALYSIS – (ANSWER ALL QUESTION IN LAB NOTEBOOK) Part II Position vs. Time Graph Matching 1. Describe how you walked for each of the graphs that you matched. (You should already have this question completed!!!) 2. Explain the significance of the slope of a position vs. time graph. Include a discussion of positive and negative slope. 3. What type of motion is occurring when the slope of a position vs. time graph is zero? 4. What type of motion is occurring when the slope of a position vs. time graph is constant? 5. What type of motion is occurring when the slope of a position vs. time graph is changing? Test your answer to this question using the Motion Detector. 6. Return to the procedure and complete Part III. Part III Velocity vs. Time Graph Matching 7. Describe how you walked for each of the graphs that you matched. 8. Using the velocity vs. time graphs, sketch the position vs. time graph for each of the graphs that you matched. In Logger Pro, switch to a position vs. time graph to check your answer. Do this by clicking on the y-axis and selecting Position. What does the area under a velocity vs. time graph represent? (You may have trouble with this question, do the best you can to answer it. We will discuss it further after the lab.) Test your answer to this question using the Motion Detector. 10. What type of motion is occurring when the slope of a velocity vs. time graph is zero? 11. What type of motion is occurring when the slope of a velocity vs. time graph is not zero? Test your answer using the Motion Detector. 15 HW #2 CONCEPTS OF PHYSICS Name___________________ Motion Graphs Period_________ The following questions pertain to Graph #1. 1. Describe what is happening in each segment. A B C D E 2. What is the velocity in segment B? 3. What is the velocity in segment D? 4. Where does the object end up with respect to the origin? 5. The following questions pertain to Graph #2. 1. Describe what is happening in each segment. A B C D E F 2. 3. 4. 5. 6. 7. 8. Where does the object start out? What is the acceleration in segment A? How far does the object travel in segment B? What is the acceleration in segment C? How far did the object travel in segment D? What is the acceleration in segment E? How far did the object travel in segment F? 16 HW #2 The following questions pertain to Graph #3. 1. Describe what is happening in each segment. A B C D E 2. 3. 4. 5. What is the acceleration in segment A? What is the acceleration in segment C? What is the acceleration in segment E? If the object started 5 m behind the origin, where did it end up after 36 seconds? ******* The following questions pertain to Graph #4. 1. Describe what is happening in each segment. A B C D E F 2. 3. 4. 5. How far does the object travel in segment A? What was the acceleration in segment B? What was the acceleration in segment D? What was the acceleration in segment F? 17 HW #2 Graph # 1 Distance (m) 20 C 15 B D 10 E A 5 0 0 10 20 30 40 Time (s) Graph # 2 Velocity (m/s) 20 B 15 F E C 10 A 5 D 0 0 10 20 30 40 Time (s) 18 HW #2 GRAPH # 3 VELOCITY (M/S) 25 20 A D C 15 E 10 B 5 0 0 10 20 30 40 TIME (S) GRAPH # 4 DISTANCE (M) 14 12 10 A E D 8 F 6 4 B C 2 0 0 10 20 30 40 TIME (S) 19 20 21 STUDY GUIDE WRITE A COMPLETE DESCRIPTION OF THE MOTION GIVEN IN EACH GRAPH AND ANSWER ALL QUESTIONS. (SEPARATE SHEET OF PAPER) Distance vs Time 10 Distance (m) 5 0 0 10 20 30 40 -5 -10 -15 Time (s) 1. 2. 3. 4. 5. 6. 7. 8. What is the velocity of segment A? What is the velocity of segment B? What is the velocity of segment C? What is the velocity of segment D? What is the velocity of segment E? What is the velocity of segment F? What is the velocity of segment G? At the end of the trip, where does the object end up? 22 Velocity (m/s) Velocity vs Time 10 8 6 4 2 0 -2 0 -4 -6 -8 -10 10 20 30 40 Time(s) 1. 2. 3. 4. 5. 6. 7. 8. What is the acceleration in segment A? What is the acceleration in segment B? Where does the object start out? What is the acceleration in segment D? How far does the object travel in segment E? What is the acceleration in segment F? How far does the object travel in segment G? If the object started out 4.5m beyond the origin, where did it end up? 23 Understanding Motion Graphs 24 9. The total distance a lab cart travels during specified lengths of time is given in the following data table. Time (s) 0.0 1.0 2.0 3.0 4.0 5.0 Distance (m) 0.00 0.32 0.60 0.95 1.18 1.45 a) Plot the distance vs. time from the values given in the table and draw curve that best fits all points. b) Describe the resulting line c) According to the graph, what type of relationship exists between the total distance traveled by the lab cart and the time? d) What is the slope of this graph? e) Write an equation relating distance and time for this data. 25