LAB 06: Impulse, Momentum and Conservation PURPOSE Investigate the relation between applied force and the change in momentum Investigate how the momentum of objects change during collisions BACKGROUND The motion of an object is often wrongly synonymous with the object s momentum. Momentum is the product of the object s mass and velocity, p m v, and since it is a vector it is in the same direction as the velocity of the object. The motion of an object and therefore the momentum of an object can be changed by applying a Force. In the first part of this lab activity, you will discover how net force and the way it is applied relate to the change in momentum of an object. When an object interacts with another object momentum can be transferred from one to another. In the second part of this lab you will discover how momentum and velocity are transferred during interactions (in this case different types of collisions). We will also be looking at how the sum total of the velocities and momenta of all the objects in the system change during the interaction. New Terms: Momentum = moving inertia = product of mass and velocity = mass velocity MATERIALS Windows PC with LoggerPro Software and Vernier Dual Force Range Meter Dynamics track with two dynamics carts, super pulley and two motion detectors mass for dynamics cart (optional) Fan attachment for dynamics carts (optional) hanging brass mass (optional) attachment string for pulley PROCEDURE In this lab, you should write all values taken in your lab notebook. Only enter them into the accompanying data table for your write up of the lab. If you collect data directly into the provided data table and not your lab notebook you will lose 10 points on your lab report grade. First we need to determine the values of the constants given. The values of the masses of the carts and the masses are displayed on them. Record them in your notebook. Also make sure you sketch each setup and label what pieces have what mass. Lab 06: Impulse, Momentum and Conservation 1/6
Figure. 1 Experiment A: How does force affect momentum 1. Measuring the Force of the Fan. The fan attachment should already be on your cart, if it is not get your teacher or lab assistant. Place the cart up against the Force sensor as shown. Open the LoggerPro File on your flash drive labeled "M2Lab06-momentum" in the HonorsLoggerProFiles folder. Make sure to ZERO the force probe. Turn on the fan and hit and let the fan run for about 10 seconds. Figure. 2 2. You will see a graph of the force felt by the probe due to the fan. This force reading will probably be a little Figure. 3 jittery, so we will be using an average. Highlight most of the graph and select the STAT button and look for the mean (average). This is the value of the average force supplied by the interaction with the fan and the air that we will use so record it in your notebook. 3. How force affects velocity and momentum. Remove the Force probe and aim cart at the RED motion detector as in Figure 1. Turn on the fan, hit and let the cart go. You should produce a graph similar to Figure 4. Use the EXAMINE button to determine the velocity and time of two good points during the motion and record them in your notebook. 4. Repeat this process 1 more time, taking down all data in your Figure. 4 notebook. After that, add the block mass to the cart and repeat the process one more time. When you are done you should have Average Force data from the fan, and three sets of numbers, a beginning velocity and time and an end velocity and time for each of three trials. 5. Before you move on, take the mass of the Cart with the fan attached as well as the mass of the block. When you have all these numbers and feel comfortable with them, move on to part B. If you don't like the way some of your graphs look, do another trial or two. Lab 06: Impulse, Momentum and Conservation 2/6
magnet sides Experiment B: Conservation of Momentum Figure. 5 1. Place the second cart on the track as shown in Figure 5. Carefully remove the fan from the first cart, you will not need in for Experiment B. Orient the carts so the magnetic ends are facing each other. Place a second Motion Detector at the other end if it is not there already. 2. Switch to Page 2: B Conservation of the LoggerPro file that is already open. Select to test that the carts are being detected and take note which color graph is for which cart (they should be color coded). Make sure to take down the masses of the carts (including the metal brackets if you have any) in your lab book. If the masses are not known, bring them to the front to mass them. 3. Place cart A (left) near the middle of the track. Start cart B (right) near the right motion detector. Click and gently push cart B leaving cart A at rest. Allow it to collide with the cart A that is at rest and continue to take data. Stop each cart before they hit the detectors (NOTE: this is considered trial (A) on your data sheet) 4. Using the graphs, determine the initial velocities just before the collision and the final velocities just after the collision. To do this, select the Examine button, and slide it across the screen until you are on a point just before the collision (see Figure 6). Record the values then slide it to a point just after the collision and record those values. Before Collision Figure. 6 5. Repeat steps 2-3 for the following situations. Make a prediction in your notebook about what will happen first. Record all data in your lab notebook. For better data, make sure the collision is clean and the carts stay on the track and do not actually touch. Push them lightly, if they are moving too fast the collision will knock them off of the track. b) Push cart A into cart B at rest (the reverse of (a)). c) Add the block mass to cart A and tighten it down. Push cart A into cart B at rest. d) Leave the mass on and push both cart B and cart A into each other at the same speed. e) Push cart A and cart B into each other but push cart A faster that cart B. f) Push cart A and cart B into each other but push cart B faster that cart A. g) Remove the block mass and push cart A and cart B into each other at the same speed. h) Align the carts so the VELCO sides are facing each other, you will have to move the brackets to the other side of the carts. Push cart A into cart B at rest. i) Using the plunger, explode cart A and cart B from rest. After Collision Lab 06: Impulse, Momentum and Conservation 3/6
ANALYSIS In calculating some of these values, it might be helpful to write an MS Excel program to repeat the calculations for you. Do this and email it to me for a little extra credit. Experiment A 1. Calculate the change in velocity for each trial and enter in the data table. 2. Calculate the Impulse (J = F t) for each trial and enter in the data table. 3. Calculate the change in momentum (p = m v) 2 x1 x2 4. Calculate the percent difference between the change in % difference 100% x momentum and the impulse. To do this use the equation 1 x2 5. What does this tell you about how impulse is related to the change in momentum during a collision? 6. What sources may have contributed to any error in your measurements? Experiment B 1. For each trial, determine the total momentum before the collision and the total momentum after the collision. Enter them in the data table as p i(total) and p f(total). 2. What does it mean to have positive momentum? A negative momentum? 3. For each trial, determine the combined total velocity before the collision and the combined total velocity after the collision, labeled v i(total) and v f(total) 4. Calculate the percent difference between the sum of v i(total) and v f(total) for Cart A and Cart B and enter it into the data table. 5. What does this tell you about the total velocity of a system before and after a collision? Is total velocity conserved? Why or why not? 6. Are there any cases when total velocity is conserved? Why might this be? 7. Calculate the percent difference between p i(total) and p f(total) using the same equation as above and enter it into the data table. 8. What does this tell you about the total momentum of a system before and after a collision? Is total momentum conserved? Why or why not? 9. What does this tell you about the total momentum of each object in a system before and after a collision? Is the momentum of each object conserved? Why or why not? 10. What sources may have contributed to any error in your measurements? Experiment C (Computer Simulation) (A) For Repeat 1 trial for experiments (a h) skip i using the computer simulation found at http://mrmaloney.com/mr_maloney/simulations/sims.html under 1D collision. *NOTE: Set e = 0 to simulate using the Velcro. (B) Answer questions 1-8 using the data from the simulation and enter it in the second data table. (C) How do your results from the lab compare with your results from the simulation? Lab 06: Impulse, Momentum and Conservation 4/6
OBSERVATIONS AND DATA cart A mass (kg): cart B mass (kg): Cart with Fan (kg): block mass (kg): Experiment A: Impulse Momentum Force [N] t [sec] v F t [N s] m v [kg m/s] % diff 1 2 3 Experiment B: Conservation of Momentum m A m B v Ai v Bi P Ai P Bi v Af v Bf P Af P Bf v i(total) v f(total) p i(total) P f(total) Diff in total v Diff in total p a b c d e f g h i Lab 06: Impulse, Momentum and Conservation 5/6
Experiment C: Conservation of Momentum using Simulation m A m B v Ai v Bi P Ai P Bi v Af v Bf P Af P Bf v i(total) v f(total) p i(total) P f(total) diff in total v Diff in total p a b c d e f g h Lab 06: Impulse, Momentum and Conservation 6/6