3.2 Forces and Motion

Transcription

1 3 DYNAMICS NEWTON S LAWS 3.2 Forces and Motion Name: 3.2 Forces and Motion So far in this course, we have analyzed the motion of objects, but have not yet discussed what might make an object move or change how it is moving. In this activity, you will try to figure this out for yourself, how forces relate to motion, and then test your predictions. It does not matter whether your initial model is correct or not we want you to feel free to try to analyze the situation in your own way, and develop your own model for explaining forces and motion. Do not search for the correct answer in a textbook, online, etc. You will have time to carefully discuss your ideas amongst your group (and between groups if you want), so there is no need to rush. What we want is for you to experience the scientific process that you really think about what is going on, that you can come up with a model to explain it, and try to justify your model. Later in this activity, when you carry out experiments to test your model, we want you to be able to analyze the data to figure out for yourself whether your model is correct or not. That is our goal here we want to focus on the process of forming a model to explain observations, and testing that model (i.e., the scientific method). Remember that we represent forces as vectors they have magnitude (the strength of the force) and direction. We will start out by considering the case of a cart being pushed by a hand such that the cart moves at constant velocity. Each group should have a cart and a track, to carry out tests for themselves Observations Try to push the cart on the track at constant velocity. Let each member of your group take turns doing that. While doing so, pay attention to how hard you are pushing the cart. 1. Think about all of the forces acting on the cart both from objects touching the cart, and objects that may be exerting a force without touching it. Discuss amongst your group how the forces should relate to the constant velocity motion. Then, draw free body diagrams below representing each of the forces acting on the cart at three successive times, t 1, t 2 and t 3 (so t 2 comes after t 1, etc.), with the assumption that the cart is moving at constant velocity the entire time. t 1 t 2 t 3 81

2 3.2 Forces and Motion 3 DYNAMICS NEWTON S LAWS 2. Explain your thought process in deciding what forces are acting on the cart, and how big they should be at each time. Do all of your group members agree with this? It is perfectly ok to have disagreement within your group. If you do not all agree, what are the different ideas being considered? (use extra paper if necessary) Now, let s consider a second case the case of constant acceleration. First, try to make the cart accelerate at a constant rate with your hand (make sure it doesnt go flying off the end of the table!). Let each group member take a turn. 3. Again, think about all of the forces acting on the cart. Discuss amongst your group how the forces should relate to each other, in order to produce a constant acceleration. Draw free body diagrams of the forces acting on the cart at three successive times, indicating the magnitude and direction of each force. t 1 t 2 t 3 82

3 3 DYNAMICS NEWTON S LAWS 3.2 Forces and Motion 4. Explain your thought process in deciding what forces are acting on the cart, and how big they should be at each time. Again, do all of your group members agree with this? If you do not all agree, what are the different ideas being considered, and why? Now let s consider a third and final case. Consider the case of a cart given a brief push and then released (so your hand will not continue pushing the cart). Think about forces acting on the cart during the push, and then after the cart has left your hand. Again, let each group member push the cart, and then discuss what is going on. 5. Think about all of the forces acting on the cart. Discuss amongst your group how the forces should relate to each other during and after the push, and also discuss what the motion of the cart is (i.e. is it constant velocity? Constant acceleration? Neither?). Draw free body diagrams of the forces acting on the cart at three successive times during the push, and then two times after the push. t 1 (during push) t 2 (after push) t 3 (later after push) 83

4 3.2 Forces and Motion 3 DYNAMICS NEWTON S LAWS 6. Explain your thought process in deciding what forces are acting on the cart, and how big they should be at each time. Again, do all of your group members agree with this? If you do not all agree, what are the different ideas being considered, and why? 7. How would you describe the velocity and acceleration of the cart after it has left your hand? 8. Based on your free body diagrams, create and describe an overall model that relates the forces acting on an object to the motion of the object. If there is disagreement within your group, describe the different models being discussed. 84

5 3 DYNAMICS NEWTON S LAWS 3.2 Forces and Motion Testing your Hypothesis Let s carry out some experiments to test your predictions of how forces on an object relate to the object s motion. To gather meaningful data, you will not only use a motion detector to measure the position (and then calculate velocity and acceleration) of an object, but also a force probe to measure the force acting on the object. This will allow us to make synchronized plots of force, position, velocity, and acceleration vs. time. For the experiment, you will first look at the case of a cart attached to a mass by a string hung over a pulley, as shown to the right (FP is the force probe). You can gather your supplies from the countertop you will need a cart, track, pulley, set of masses, and string. To take data, you will also need a motion detector and force probe. Before beginning your experiment though, let s consider what is going on. Since the force probe (FP) and cart (with mass m 1 ) are attached together, we can treat them as one object (henceforth the cart will refer to the cart and force probe together). 9. Draw a free body diagram of the cart at three different points in time. A key thing to consider will the pulling force on the cart from the string be constant, or change in time? t 1 t 2 t 3 85

6 3.2 Forces and Motion 3 DYNAMICS NEWTON S LAWS 10. Sketch below what you expect the position, velocity, acceleration and force vs. time graphs to look like. Note that the force probe will only be measuring the pulling force the string exerts on the cart. x [m] v [m/s] a [m/s 2 ] F [N] 11. Explain why you expect to see the graphs that you drew in the previous problem. Focus on your theorized relationship between force and motion. Okay, time to carry out the experiment. First, make sure the track is level! The easiest way to do this is to set the cart on the track without the mass pulling it towards the pulley if it rolls on its own, then the track is not level. Adjust the track until the cart will not roll on its own when released from rest. Start up Logger Pro on the computer, and make sure you have graphs to show force, position, velocity, and acceleration. Also make sure that both the force probe and motion detector are connected to the computer. Start out by hanging a 10 gram mass from the end of the 86

7 3 DYNAMICS NEWTON S LAWS 3.2 Forces and Motion string. Have one group member hold the cart in place until someone clicks Collect on Logger Pro to start collecting data. 12. Draw the force, position, velocity, and acceleration vs. time graphs produced by Logger Pro below. x [m] v [m/s] a [m/s 2 ] F [N] 13. How do these compare to your predictions? Are there any surprises? If so, discuss these with your group members, and summarize that discussion below. 87

8 3.2 Forces and Motion 3 DYNAMICS NEWTON S LAWS 14. Highlight the portion of the position or velocity graph corresponding to the time period when the cart was being pulled by the falling hanging mass, and determine the acceleration. What do you get? Is the acceleration fairly constant? Is it changing? If so, how? If it is a constant value, what is it? 15. What do you think might happen if you double the weight of the hanging mass to 20 grams? What should the graphs look like (describe, you can draw if it helps you describe them)? In particular, what do you expect for the acceleration and velocity, compared to the first run? And do you expect the force probe s reading to exactly double? 16. Carry out the experiment with a 20 gram hanging mass, and see what your results are. What is your acceleration now? Is it what you expected? If its not exactly what you expected, discuss why that may be, and summarize that discussion below. 88

9 3 DYNAMICS NEWTON S LAWS 3.2 Forces and Motion 17. Did the force reading change exactly as you expected? Do you have any thoughts as to why? Discuss. 18. Now, add a 250 gram mass to the cart (keep the 20 gram hanging mass). What do you expect to happen to the various readings, compared to the last run? 19. Carry out the experiment, and determine the average acceleration and force. How do they compare to your expectations? Discuss and summarize. 89

10 3.2 Forces and Motion 3 DYNAMICS NEWTON S LAWS 20. Based on the experiments that you have done, what can you conclude about how forces are related to motion? In particular, did you confirm or disprove your hypothesis? Are all members of your group in agreement about the implications of the experiments? 90