1 D Collisions and Impulse

Transcription

1 SP211 Lab: Six 1-D Collisions and Impulse PHYSICS LAB 6 SP211 1 D Collisions and Impulse I. Introduction A. Linear momentum is an important physical quantity associated with motion. In fact, Newton actually wrote his second law (N2L) in terms of linear momentum. Specifically, the most general statement of N2L is: The time rate change of the linear momentum of a particle is equal to the net force acting on the particle. (Note: For the remainder of this laboratory the term "momentum" is an abbreviation for "linear momentum.") dp F Fnet dt B. A related quantity is impulse. Impulse can be calculated when we know how the force varies with time and is important because it is equal to the change of momentum. Finally, for an isolated system (i.e., there is no net external force acting on it), N3L requires that the net impulse be zero and this gives rise to the law of conservation of momentum. In this laboratory, we will carry out several experiments designed to help us better understand these quantities. II. Objectives At the end of this activity, you should: 1. Understand, observe, and calculate the Conservation of Linear Momentum for an Elastic 1 D Collision. In addition, understand and graph the impulse created. 2. Understand, observe, and calculate the Conservation of Linear Momentum for an in elastic 1 D Collision where each mass is equal. 3. Understand, observe, and calculate the Conservation of Linear Momentum for an in elastic 1 D Collision with different masses. Page 1 of 6

2 SP211 Lab: Six 1-D Collisions and Impulse III. Needed Equipment Your instructor will show you the experimental setups, which consists of lab equipment that should be familiar with by now, consisting of a motion sensor (MS), force sensor (FS), track, springs, iron weights, and carts; also string and a pulley for calibration of the FS. Experiment 1 Experiment 2 Experiment 3 IV. Procedure A. Discussion: Collisions and Conservation Theorems: Total momentum is conserved in all collisions. (Why?) Kinetic energy is conserved in elastic collisions. (Why?) In completely inelastic collisions, the colliding bodies final velocities are the same. B. Preliminary Data: B.1. Measure and record the masses of your carts and keep track of which one is which. C. Connect the MS to the Lab Pro and set up Logger Pro Check that everything is plugged in correctly: the MS into DIG/SONIC2 and the FS into CH 1 Page 2 of 6

3 SP211 Lab: Six 1-D Collisions and Impulse Recurring steps: Using Logger Pro to program the LabPro: Known as the Three Steps Experiment > Set Up Sensors > Show all Interfaces: Make sure all the right sensors show up in all the right holes. Experiment > Data Collection: Set the length of time data is to be taken and the rate at which data is to be taken. Here, since the collision will happen very quickly we need to take data often enough or we might not take data when the collision occurs; thus you should set for approx. 50 samples/sec (30 samples/sec at a minimum). File > Settings for...: Check the checkbox to Show Zero on Toolbar, and make sure number of points for Derivative and Smoothing are both 7. It is necessary to calibrate the FS any time that we start LoggerPro. In case you do not recall the procedure for calibration, it is as follows: Attach the FS to the track. Place a pulley at the high end of the track and hang the 200g weight from it. Under the Experiment menu, click on Calibrate. Then Select CH1: Dual Range Force and click on Calibrate now. For Reading 1, wait for the voltage reading to become steady, change Enter Value to 1.96N (which is the weight of the 200g mass). Click the Keep button. For Reading 2, hang the 500 g mass from the hook located on the Force Sensor. Wait for the voltage reading to become steady, and then change Enter Value to 4.9 (which is the weight of the 500g mass) and click the Keep button. Click the Done button. Page 3 of 6

4 SP211 Lab: Six 1-D Collisions and Impulse D. Experiment 1. Elastic Collision with a Stationary Target: Impulse Momentum Theorem D.1. Attach your force sensor (FS) to the bracket and attach the bracket to the track so that the FS is fixed to the track securely. D.2. Follow the Three Steps in Logger Pro to program your LabPro to measure the motion of a cart on the track, and the force the cart exerts on the FS during the collision. D.3. Calibrate the FS just before you start the experiment, and then carefully remove the FS hook and replace the hook with your weak spring. (Do not use the strong spring.) D.4. Measure the motion of the cart just before and just after it collides with the weak spring, and measure the force exerted by the cart on the spring during the collision. D.5. Use Analyze > Linear Fit on the position vs time data to measure the velocity of the cart just before and just after the collision. Check your work by using Analyze > Statistics on the velocity vs time data. Do these velocities agree, as they should? D.6. Use Analyze > Integral on the force vs time graph to determine the impulse delivered to the cart. J D.7. Use your measurements to test whether or not your data agree with the Impulse Momentum Theorem; discuss this in a paragraph on your graph. Page 4 of 6

5 SP211 Lab: Six 1-D Collisions and Impulse E. Experiment 2. Inelastic Collision between Carts with Similar Masses: Conservation of Linear Momentum E.1. Place your second cart on the track, and make sure it is stationary. Note: Your instructor might choose to let you leave the force sensor on the track to again reinforce the Impulse = area under the Force (t) curve lesson. E.2. Measure the motion as your first cart collides in elastically with the stationary target cart. The goal is to get them to stick together due to the Velcro. E.3. As in Part D above, use both your position vs time and velocity vs time graphs to determine the velocities of the carts before and after the collision. E.4. Use your measurements to discuss whether or not momentum was conserved in your symmetric collision. F. Experiment 3. Inelastic Collision between Carts of Different Masses: Conservation of Linear Momentum F.1. Load two iron bars on one of your carts to increase its mass. Measure the new mass, and make measurements similar to the ones you made in Part E to see whether or not momentum is conserved in this non symmetric collision. Discuss your results in a short paragraph on your graph. G. Lab Report Graph from Part D, with calculations and discussion. Graph from Part E, with calculations and discussion. Graph from Part F, with calculations and discussion. Page 5 of 6

6 SP211 Lab: Six 1-D Collisions and Impulse V. Clean Up A. End of Lab Checkout: Before leaving the laboratory, please tidy up the equipment at the workstation and quit all running software. B. The lab station should be in better condition than when you arrived and more importantly, should be of an appearance that you would be PROUD to show to your legal guardians during a Parents Weekend. C. Have your instructor inspect your lab station and receive their permission to leave the Lab Room. D. You SHALL follow this procedure doing every lab for BOTH SP211 and SP212! Many thanks to Dr. Huddle for his assistance in producing this Laboratory procedure; specific references can be supplied on request. LCDR Timothy Shivok Page 6 of 6