Momentum in One Dimension

Transcription

1 Momentum in One Dimension Theory The linear momentum p of an object is defined as p = m v (1) where m is the mass of the object and v its velocity. Note that since velocity is a vector, momentum is as well. The mks unit of momentum is kg m/s. Momentum provides a convenient way to analyze collisions. If there are no (or negligible) external forces in a collision between different objects, it can be shown that momentum is conserved. The easiest collision to analyze is that between two objects in one dimension; in this case, the momenta are scalars. This is the type we will analyze in this experiment. Consider two carts moving on a track. Conservation of momentum dictates that the total momentum before a collision is equal to the total momentum after the collision. The velocities v 1o and v 2o are before the collision; v 1f and v 2f after. m 1 v 1o + m 2 v 2o = m 1 v 1f + m 2 v 2f (2) Apparatus Dynamics track, Carts, Load masses, Elastic bumpers, Computer, Pasco 750 interface, Motion sensors, Capstone software. Procedure The collisions take place on a dynamics track to which two motion sensors are attached. The sensors measure position and time data for each cart and use this to display a graph of Velocity vs. Time. The velocities both before and after the collision are determined from this graph. To ensure good data: Make sure that the track is level; the carts should not roll without being pushed. Practice each collision a few times before collecting data; several people should be involved in collecting the data - each with a specific function. Make sure that both carts remain on the track both before and after the collision. The motion sensors use ultrasonic signals - keep objects away from the track as much as possible while collecting data. 1

2 Open Capstone and the activity entitled Conservation of Linear Momentum. Data collection proceeds as follows: 1. Set the carts in their pre-collision positions. Click the Record button and give the carts their initial velocities. Click the Stop button after the collision, just before the carts strike the bumpers in front of the sensors. 2. If the collision area of the graphed data is too small to analyze effectively, use the Select Range and Resize tools to enlarge it. 3. Use the Delta tool to determine the velocities of the carts before and after the collision. The motion sensor will sometimes display a spurious point (out of line with the ones surrounding it), so be careful when determining the velocities. You expect a relatively constant velocity just before and just after a collision. This is shown in Figure 1. Figure 1: Left cart velocity determined as m/s after a collision. 2

3 Elastic Collisions Turn the carts so that the magnet ends will meet when they collide - this will approximate an elastic collision. As you look at the track from the computer side of the table, the cart on the left will be Cart 1 and the one on the right Cart 2. The carts and load masses each have a mass of 500g. Perform the following collisions: 1. The carts should be empty; i.e., no load masses. Send Cart 1 toward Cart 2, initially at rest near the center of the track. Place the data for this collision below. 2. Place one of the load masses in Cart 2 and repeat the first collision. Place the data for this collision below. 3. Keep the load mass in Cart 2. This time, start with the carts at opposite ends of the track and send them toward each other. Place the data for this collision below. v 2o (m/s) 3

4 Inelastic Collisions Turn the carts so that the Velcro ends will meet when they collide - they should remain stuck together after the collision. Note that the separate velocities after the collision have been replaced with a single combined velocity v cf. Perform the following collisions: 1. The carts should be empty; i.e., no load masses. Send Cart 1 toward Cart 2, initially at rest near the center of the track. Place the data for this collision below. v cf (m/s) 2. Place a load mass in Cart 2. Start with the carts at opposite ends of the track and send them toward each other. Place the data for this collision below. v 2o (m/s) v cf (m/s) Analysis 1. Was momentum conserved in your collisions? Why or why not? 4

5 Pre-Lab: Conservation of Linear Momentum in One Dimension Name Section Answer the questions at the bottom of this sheet, below the line - continue on the back if you need more room. Any calculations should be shown in full. 1. An object of mass 3.00kg is moving with a velocity of 6.00m/s. What is the magnitude of its momentum? 2. An object of mass 3.00kg traveling to the right with velocity 6.00m/s collides head-on with a second object of mass 5.00kg initially at rest. After the collision, the 3.00kg mass has a velocity of 1.50m/s to the left. What is the velocity and direction of the 5.00kg mass? 5