PHY 211:

Laboratory # 8: Collisions

An interaction between 2 moving objects that lasts a very short time is called collision. During a collision, the total momentum of the system is conserved. During this lab, you will analyze 2 different types of collision:

-the totally inelastic collision ( the 2 objects stick together after the collision). During the totally inelastic collision, only the total momentum is conserved.

-the elastic collision . If the collision is perfectly elastic, the momentum and the total kinetic energy are conserved.

Objectives:

  • to study different types of collision
  • to verify the law of conservation of momentum during collisions
  • to analyze the transfer of kinetic energy during a collision

Materials

  • Nikon 200CoolPix camera
  • Low friction ramp
  • Dynamic carts
  • LoggerPro software
  • Meter stick
  • Digital scale.

Preliminary Experiments and Questions:

Adjust your low-friction ramp until it is perfectly horizontal (use a level)

On the low-friction ramp, perform the following experiments and describe the momentum vectors for each object before and after the collision

A. Elastic collisions. For the following experiments, the 2 carts will have the magnets facing each other. The magnets repel each other so the carts do not touch each other during the collision, which eliminates the friction at contact. The collision is almost perfectly elastic .

  1. A cart collides with a cart of equal mass that is at rest
  1. A heavy cart collides with a lighter cart that is at rest.
  1. Two carts of equal masses moving toward each other at different speeds
  1. Two carts of different masses moving in the same direction at different speeds.

B. Inelastic collisions. During the following experiments, the 2 carts will have the Velcro sides facing each other, so as the 2 carts will remain attached after the collision ( totally inelastic collision)

  1. A heavy cart moving toward a light cart that is at rest
  1. Two carts of equal masses colliding head-on.

Procedure:

Part I. Making the movies

You will use the Nikon camera to obtain 2 digital movies for an elastic and inelastic collision, respectively. You can choose equal or different masses, equal or different velocities, carts moving toward each other or in opposite directions.

  1. Using a level, make sure that the ramp is horizontal
  2. Find the masses of the 2 carts using the digital scale. If you are using additional weights, enter the total mass below

M1=______M2=______

  1. Place pieces of black tape on the ramp on the 0 and 100 cm markings. You will use this distance to scale the movie. Place pieces of black tape on the carts, to make sure that you place the pointer in the same place when analyzing the movie.
  2. Using the digital camera, record an inelastic and then an elastic collision. Review the movies to make sure that several frames before and after the collision are recorded.
  3. Turn the camera off. Connect it to the USB port of the computer and turn it on. The “ New Hardware Found” message will pop up. Wait until the message “ New hardware installed and ready to use” is displayed, and then close the message window.
  4. From “My Computer”, open F:/Nikon/DCIM/100Nikon. Click and drag to move your movies on the desktop.
  5. After the movies are copied on the desktop, double click on the right-bottom corner “Safely remove hardware”. Follow the prompts to disconnect the camera.

Part II Analyzing the movie

  1. Inelastic collision
  1. Open Programs/Vernier Software/LoggerPro 3.3. Close the “Tip of the day” and then select Insert/Movie. Open your inelastic collision movie from the desktop
  2. Using the ► icon at the bottom of the screen, play the movie. Using the ▀ icon, stop the movie about 5 frames before the collision.
  3. Click on the right-bottom icon to view a vertical toolbar. To scale the movie, click on the icon from the vertical toolbar.Click and drag from the 0 to the 100cm marking on the ramp. In the pop-up window, enter the length of the object, 1m
  4. Select your pointer by clicking on the icon. Click on the black piece of tape of the first cart. The movie will advance by one frame. Continue to click on the first cart after the collision (about 5 frames before and about 5 frames after the collision). When you are done with the first cart, Click on the icon again to de-select the pointer
  5. To select a different pointer for the second cart, click on icon. The second pointer will be selected
  6. Click on icon and repeat step 4 for the second cart. The point markers will have a different color on the screen for the second cart.
  7. Deselect the pointer and minimize the movie window .
  8. Click on the vertical (y) axis of the graph and select the x position. The graph of the x position for the first cart will be displayed. What is the shape of the graph? Apply the appropriate type of fit for each portion and print your graphs. What is the significance of the slopes of the 2 portions of the graph? Enter your results here:
  1. Click on the vertical (y) axis of the graph and select the x velocity. The graph of the x velocity for the first cart will be displayed. What is the shape of the graph? Describe the motion of the cart before, during and after the collision.
  1. Click on the vertical (y) axis of the graph and select the x 2position. The graph of the x position for the second cart will be displayed. What is the shape of the graph? What is the significance of the slopes of the 2 portions of the graph? Apply the appropriate type of fit for each portion and print your graphs. Enter your results here.
  2. Click on the vertical (y) axis label of the graph and select the x velocity 2. The graph of the x velocity for the second cart will be displayed. What is the shape of the graph? Describe the motion of the cart before, during and after the collision.
  3. Was the velocity of the first cart constant before the collision? If not, what forces could be responsible for the change in velocity? Using a linear fit, estimate the acceleration of the cart before collision and the magnitude of the net force. Show your calculations below and print out a copy of your graph.
  4. Was the velocity after collision constant? If not, estimate the acceleration. Is this acceleration different from the one calculated in step 12 above? Explain.
  1. Calculate the total momentum before the collision and after collision. Show your calculations and enter results here:

P before=______

P after=______

  1. How do the results compare? Is the momentum conserved? Write a conclusion.
  1. Elastic collisions
  1. Repeat steps 1-9 above for the elastic collision movie. Record your results here:

M1=______M2=______

V1 before=______V2 before=______

V1 after=______V2 after=______

  1. LoggerPro can calculate the momentum of each cart. From the Data menu, select New Calculated Column. In the Name field, enter momentum 1 and in the Short Name field, enter p1 In the Equation field, enter the mass of the first cart and the symbol *, and then from the Variables menu select the x velocity. Then click Done. In the new column, the product mv1 will be calculated.
  2. Repeat step 2 for the second cart. The momentum mv2 of the second cart will be calculated.
  3. Click on the y label of the graph and select p1 and p2. The graphs p1 vs. time and p2 vs. time will be displayed. Describe the shape of the graphs.
  1. Calculate the total momentum before the collision and after collision. Show your calculations and enter results here ( Remember, momentum is a vector, so the direction of the motion is important)

P before=______

P after=______

  1. How do the results compare? Is the momentum conserved? Write a conclusion.

One last thing:

The center of mass of a system is the point that moves as though all of the mass were concentrated there and all forces were applied there. Therefore, for the center of mass the the momentum of the center of mass is constant (in the absence of friction and other external forces)

Mvcom=m1v1+m2v2

Where M is the total mass of the system and vcom is the velocity of the center of mass.

For one of the collisions above, calculate the velocity of the center of mass (Data/New Calculated Column) and graph vcom vs. time

  1. Was the vcom constant in time? If not, calculate the acceleration of the center of mass. Compare this acceleration to the acceleration calculated in step 12 above.

2. Based on your results above, estimate the effect of friction and/or incline.