Experiment 20, Modified Version:  When two objects moving in the same direction collide, the total of their momenta immediately after collision is equal to the total immediately before collision, whether or not their motion after collision is along the same line as their original velocities.

Using glancing collisions of spherical objects, which as in Experiment 19 are permitted to freely fall a known distance after collision, we can determine the angle and magnitude of the velocity of each immediately after collision and test momentum conservation for  two-dimensional collisions.

The preceding experiment will now be modified by supporting a second ball on a cut straw just past the end of the ramp. The second ball is positioned so that the two balls will collide with their centers of mass at the same vertical position, but the collision is not head-on in the horizontal plane. The horizontal distance traveled after collision will therefore have a component in the direction of the ramp and a component perpendicular to this direction. We will test momentum conservation in both directions.

Collide two balls of unequal mass (refer to modified Experiment 19 and to the video clips for the details of the setup).

• As shown on the video clip, position the 'target' ball so that its center is at the same height as the center of the moving ball, but also so that the balls do not collide 'head-on' as viewed from above.
• Define the direction of the x axis as that of the moving ball before collision, with the y axis perpendicular to this direction. Determine the distance traveled by each ball, falling as a projectile, in each direction.

From your data determine the x and the y velocities of each ball after collision, the analyze the momentum:

• Obtain two equations for m1 and m2 by setting the expressions for the total before-collision and after-collision x and y momenta equal.
• Rearrange the equation for the y momenta so that the left-hand side is m2 / m1. The right-hand side will be a pure number, representing the ratio of the two masses.
• Rearrange the equation for the x momenta so that the left-hand side is m2 / m1. The right-hand side will be a pure number, also representing the ratio of the two masses.
• To what extent are your results consistent? That is, within the limits of experimental error are the two m2 / m1 ratios equal?

Model the collision from different reference frames using MOMSIM2.

• Model the collision from the frame of reference of the first ball before collision and describe the collision from this frame.
• Model the collision from the frame of reference of the first ball after collision and describe the collision from this frame.
• Model the collision from the frame of reference of the second ball after collision and describe the collision from this frame.
• Model the collision from the center-of-mass frame of reference and describe the collision from this frame.

View the simulation KINMASS0.  

• What is the coefficient of restitution for these collisions?
• Do the collisions appear to be realistic?

Analysis of errors

• Discuss possible sources of error in this experiment.
• Estimate the possible error ranges in your data, and determine whether within the resulting ranges of observed momenta we can conclude that momentum is conserved.