Lab Force and Motion

Save your work! Name_______________________________________________Section______________________ LAB: FORCE AND MOTION Learning goals:  C l e a r l y descri b e e xp erime ntal o b serv at io n s i n w ords .  Give a p hysic al i nt er p re tat io n (i . e ., e xpla i n t he me an i ng of) th e fu nct iona l re lat io n shi p s an d co n s tant s i n a mat he mat ic al mode l of e xp erime ntal d ata.  Inf er selected phys ical law s fro m direc t e xp erime ntat ion.  Identify forces acting on objects and construct free - ‐ body diagrams.  Carry out proportional reasoning with Newton’s second law.  Reason qualitatively with Newton’s second law; i.e., infer magnitudes of forces or the motion of an object. Materials:  computer-based laboratory system  RealTime Physics Mechanics experiment configuration files  force probe  motion detector  spring scale with a maximum reading of 5 N  track  cart  500 g cube mass to attach to cart  low-friction pulley, lightweight string, table clamp, variety of hanging masses In the previous labs, you have used a motion detector to display position-time, velocity-time, and acceleration-time graphs of different motions of various objects. You were not concerned about how you got the objects to move, i.e., what forces (pushes or pulls) acted on the objects. From your own experiences, you know that force and motion are related in some way. To start your bicycle moving, you must apply a force to the pedal. To start up your car, you must step on the accelerator to get the engine to apply a force to the road through the tires. But exactly how is force related to the quantities you used in the previous lab to describe motion-- position, velocity, and acceleration? In this lab you will pay attention to forces and how they affect motion. You will learn how to measure forces. By applying forces to a cart and observing the nature of its resulting motion graphically with a motion detector, you will come to understand the effects of forces on motion. Note: Since forces are detected by the computer system as changes in an electronic signal, it is important to have the computer "read" the signal when the force probe has no force pushing or pulling on it. This process is called "zeroing." The electronic signal from the force probe can change slightly from time to 1

Save your work! time as the temperature changes. Therefore, zero your force probe with nothing attached to the probe before making each measurement. Investigation 1: motion and force You can use the force probe to apply known forces to an object. You can also use the motion detector, as in the previous two labs, to examine the motion of the object. In this way you will be able to explore the relationship between motion and force. Activity 1-1: Pushing and Pulling a Cart In this activity you will move a low friction cart by pushing and pulling it with your hand. You will measure the force, velocity, and acceleration. Then you will be able to look for mathematical relationships between the applied force, the velocity, and acceleration, to see whether either is (are) related to the force. 1. Set up the cart, force probe, and motion detector on a smooth level surface as shown below. The mass of the cart should be about 1 kg including the force probe and a 500 g cube mass. Make sure the motion detector sees only the cart and not the cable connecting the force probe to the computer. Prediction 1-1: Suppose you grasp the force probe hook and move the cart forward and backward in front of the motion detector. Do you think that either the velocity or the acceleration graph will look like the force graph? Is either of these motion quantities related to force? (That is to say, if you apply a changing force to the cart, will the velocity or acceleration change in the same way as the force?) Explain. The force graph will look like the acceleration graph. This is because when you are moving the motions back and forth, you have to reduce the force to slow it down and then add more force to put it in the opposite direction. The velocity graphs will most likely be a parabola which will not look like the motion of the force and velocity. F=ma. 2

Save your work! Question 1-1: Does either graph-velocity or acceleration-resemble the force graph? Which one? Explain how you reached this conclusion . The acceleration graph has a partial resemblance of the force graph. The force graph appears as a solid straight line, with occasional peaks and vallies at the same points where acceleration peaks and vallies. The maginitude of these are a lot smaller than the acceleration graph. The velocity had no resembelence to the graph of force. Question 1-2: Based on your observations, does it appear that there is a math e matical relationship between either applied force and velocity, applied force and acceleration, both, or neither? Explain. Yes, the force and acceleration are directly related, meaning as acceleration increases, force will also increase. This is because as the acceleration was positive and increasing, so was the force at the same time. Activity 1-2: Speeding Up Again You have seen in the previous activity that force and acceleration seem to be related. But just what is the relationship between force and acceleration? 1. Set up the ramp , pulley , cart, string, motion detector , and force probe as shown below . The cart should be the same mass as before (abo ut 1 kg). Be sure that the cart's friction is minimal. 4

Save your work! 2. Prepare to graph velocity, acceleration, and force. Open the experiment file called Speeding Up Again (L03A2-2) to display the velocity, acceleration, and force axes that follow. Prediction 1-2: Suppose that you have a cart with very little friction and you pull this cart with a constant force as shown below on the force-time graph. Sketch your prediction in Logger Pro on the axes if the force graph looks like the one below . 5

Save your work! MASS = 20 grams Questions 1-3: After the cart is moving, is the force that is applied to the cart by the string constant, increasing, or decreasing? Explain based on your graph. The force the is applied is constant throughout the entire motion. Only looking at the graph before it hit the end, the force was a straight line which means it had one constant force the entire time. Question 1-4: How does the acceleration graph vary in time? Does this agree with your prediction? Does a constant applied force produce a constant acceleration? The acceleraton graph is exactly the same shape as the force graph. It stays constant the entire time, which proves it is diretly related to the force. So, the constant applied force produces a constant acceleration. Question 1-5: How does the velocity graph vary in time? Does this agree with your prediction? What kind of change in velocity corresponds to a constant applied force? The velocity graph was constantly increasing with time. This agrees with the the prediction that force and velocity are not related. If the force is positive, the velocity increases and vice versa. 7

Save your work! Activity 1-3: Acceleration from Different Forces In the previous activity you examined the motion of a cart with a constant force applied to it. But what is the relationship between acceleration and force? If you apply a larger force to the same cart (while the mass of the cart is not changed) how will the acceleration change? In this activity you will try to answer these questions by applying different forces to the cart, and measuring the corresponding accelerations. If you accelerate the same cart with two other different forces, you will then have three data points-enough data to plot a graph of acceleration vs. force. You can then find the mathematical relationship between acceleration and force (with the mass of the cart kept constant). Prediction 1-3: Suppose you pulled the cart with a force about twice as large as before. What would happen to the acceleration of the cart? Explain. The acceleration would increase proportionally. The acceleration would increase because the force being applied would also increase. The force increasing is due to the increase in mass that is pulling it. 1. Test your prediction. Keep the graphs from Activity 2-2 persistently displayed on the screen. 2. Accelerate the cart with a larger force than before. To produce a larger force, hang a mass about two times as large as in the previous activity. Record the hanging mass: 40 grams 3. Graph force, velocity, and acceleration as before. Don't forget to zero the force probe with nothing attached to the hook right before graphing. 4. Insert your graphs on the next page. 8

Save your work! 8. Find the mean acceleration and force, as before, and record the values in the bottom row of Table 1-1. Activity 1-4: More Acceleration vs. Force Data Gather data for average acceleration and average force for several other forces applied to the same cart. Add additional rows to Table 1-1 . Activity 1-5: Relationship Between Acceleration and Force In this activity you will find the mathematical relationship between acceleration and force. 1. Use the graphing routine in the software to plot a graph of acceleration vs. force from the data in Table 1-1. To plot the graph load the experiment file called Acceleration vs. Force (L03A2-5), and enter your data in the table. You may wish to adjust the graph axes, after all of the data are entered, to better display the data. 2. Use the mathematical modeling techniques that you have developed to determine the best model for the data relating acceleration of the cart and the applied force. Display your equation on the graph Y=-.2415x + .055 10

Save your work! 3. Insert your graphs below. Question 1-8: Does there appear to be a simple mathematical relationship between the acceleration of a cart (with fixed mass and negligible friction) and the force applied to the cart (measured by the force probe mounted on the cart)? Write down the equation you found and describe the mathematical relationship in words. A linear relationship works best and the equation is y=mx+b. Question 1-9: If you increased the force applied to the cart by a factor of 10, how would you expect the acceleration to change? How would you expect the acceleration-time graph of the cart's motion to change? Explain based on your graphs. Yes, if the force of the graph increased by a factor of ten, then the acceleration will also increase. The constant of the acceleration would increase on the graph. For instance, if the force was 1N and the acceleration was 1m/s^2, then the force change to 10N, the acceleration would change accordingly and would be 10m/s^2. Question 1-10: If you increased the force applied to the cart by a factor of 10, how would you expect the velocity-time graph of the cart's motion to change? Explain based on your graphs. The velocity would decrease since they are inversely related. This means when the force increases, the velocity decreases. This is shown in the graphs above where the velocity is the opposite of the force graph. 11

Save your work! If the positive x direction is toward the right, what are the signs of the velocity, force, and acceleration after the cart is released and is moving toward the right? Velocity Force Acceleration 2. Test your predictions. Use a hanging mass that causes the cart to move all the way across the ramp from right to left in about 2–3 s when the mass is released. Record the hanging mass that you decided to use: 20 grams 3. Open the experiment file called Slowing Down Again (L04A1-1) to display the axes that follow. 4. Test to be sure that the motion detector sees the cart during its complete motion, and that the string and force probe cable are not interfering with the motion detector or the motion of the cart. 5. As usual, the positive x direction is chosen to be away from the motion detector—toward the right. Since a push on the force probe now is a force toward the right, and is therefore positive, the software has been set up to make a push positive (and a pull negative). 6. As always, zero the force probe with nothing pulling on it just before each graph. Begin graphing, and when the motion detector starts clicking, give the cart a short push toward the right and then let it go. Be sure to keep your hand out of the region between the motion detector and the cart. Stop the cart before it reverses its direction. After you have collected good graphs, move your data so that the graphs are persistently displayed on the screen for later comparison. 7. Insert your velocity, acceleration, and force graphs here. 13

Save your work! Question 1-11: Did the signs of the velocity, force, and acceleration agree with your predictions? If not, can you now explain the signs? Yes, the force and acceleration was negative in the positive direction and positive when moving in a negative direction. The velocity was positive when moving in the positive direction and negative when moving in the negative direction. Question 1-12: Did the velocity and acceleration both have the same sign? Explain these signs based on the relationship between acceleration and velocity. The velocity and acceleration had opposite signs until the velocity began to move in the negative direction. When the velocity was positive it was slowing down which means the acceleration is negative, then when it was traveling in a negative direction it was speeding up so acceleration and velocity is both negative. Question 1-13: Did the force and acceleration have the same sign? Were the force and acceleration in the same direction? Explain. The force and acceleration had the same sign. This is because they were in the same direction. And acceleration causes the magnitude and direction of force to change. Question 1-14: Based on your observations, draw below vectors that might represent the velocity, force, and acceleration for the cart at the same instant in time. Velocity Force Acceleration Do these agree with your predictions? If not, can you now explain the directions of the vectors? Yes, this is the exact same as the predictions. Question 1-15: After you released the cart, was the force applied by the hanging mass constant, increasing, or decreasing? Explain why this kind of force is necessary to cause the observed motion of the cart. The force of the mast increased as the acceleration increased and decreased as the acceleration decreased. However, it was constant for a period of time, then changed directions, then constant back in the other direction. Activity 1-7: Speeding Up Toward the Motion Detector Using the same setup as in the last activity, you can start with the cart at the right end of the ramp and release it from rest. It will then be accelerated toward the motion detector as a result of the force applied by the falling mass. Prediction 1-7: Suppose that you release the cart from rest and let it move toward the motion detector. Draw on the diagram below vectors that might represent the velocity, force, and acceleration of the cart at each time after it is released and is moving toward the left. Be sure to mark your arrows with v, F, or a as appropriate. Assume that the cart is already moving at t 1 . 14

Save your work! Question 1-16: Which of the signs—velocity, force, and/or acceleration—are the same as in the previous activity where the cart was slowing down and moving away, and which are different? Explain any differences in terms of the differences in the motion of the cart. The acceleration is the same as the last time graph. This is because they are moving toward the sensor and speeding up. Question 1-17: Based on your observations, draw below vectors that might represent the velocity, force, and acceleration for the cart at the same instant in time. Velocity Force Acceleration Do these agree with your predictions? If not, can you now explain the directions of the vectors? The force one does not agree with my prediction, the force is positive here. The difference is because it is a positive force being applied to cause it to speed up in this direction. It is the magnitude. Question 1-18: Write down a simple rule that describes the relationship between the direction of the applied force and the direction of the acceleration for any motion of the cart. They are directly related. If acceleration is negative, the force will also be negative and vice versa. 16

Save your work! Question 1-19: Is the direction of the velocity always the same as the direction of the force? Is the direction of the acceleration always the same as the direction of the force? In terms of its magnitude and direction, what is the effect of a force on the motion of an object? No, the velocity is the opposite of the force. The acceleration is always the same as the force. The magnitude of the force increases velocity and acceleration. 17

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Save your work! Question 2-3: Describe what you did, and compare the motions of the cart. Question 2-4: Draw arrows next to the diagram above that represent a scale drawing of the magnitudes and directions of A F  , B F  , and net F  . Again let 5.0 cm of arrow length represent each newton of force. 3. Observe what kind of motion results when two spring scales are hooked to opposite ends of the cart and extended in a horizontal direction so that each of their forces is equal to 1.0 N in magnitude, but they are opposite in direction. Question 2-5: Does the cart move? If so, how? What do you think the combined or net applied force on the cart is equal to in this situation? Question 2-6: Draw arrows next to the diagram above that represent a scale drawing of the magnitudes and directions of the forces you are applying. Let 5.0 cm of arrow length represent each newton of force. Label each arrow appropriately with an A F  or an B F  . Question 2-7: Do one-dimensional forces seem to behave like one-dimensional vectors? Why or why not? 20