# What is the proportionality between volume and momentum passed on in a collision?

I am designing a simple experiment with a setup as follows Simply put, I am rolling a marble into a light plastic bucket (cup) and seeing how far it swings in a ballistic pendulum. I can get the speed of the marble on its own and the marble + bucket through certain equations or video playback and the grid paper. However, I am changing the masses of the marble, and I am wondering how that affects the momentum change from the marble on the ramp to the marble and the bucket on the ballistic pendulum.

Since I know that this does not follow the principle of conservation of momentum due to net external forces such as friction and air resistance (albeit small because it is a glass sphere), I'm assuming the momentum will theoretically change. Realistically, this may or may not be true.

However, I do not know if the size affects the momentum lost. For example, would a 20% bigger marble lose 20% more momentum when it actually goes into the bucket? My current theory is based upon the fact that a glass marble sees relatively little friction anyway, and even if the size is increased, the sphere's contact with the surface is still very small. On top of that it is an aerodynamic shape to begin with so a change in volume should not increase air friction too much either. Therefore, I believe that a larger marble would lose less momentum, and pass on more of its original momentum into the bucket, as friction proportionally affects it less. However, I am not sure if this makes any sense.

In terms of kinetic energy, I have also used my knowledge to hypothesize that more momentum will pass on more kinetic energy (and therefore momentum) to the bucket. Since the collision is somewhat elastic too, that kinetic energy will be also passed back into the ball which could possibly be a big factor (?), (some may go into deforming the bucket, but that is less likely since rigid plastic is hard pressed to get deformed by a marble).

Hopefully, I have explained it well enough using the lab setup, so I'd like to simply phrase my entire question in one sentence here: Is there a proportionality between the volume of a marble, and momentum it is able to pass on into a ballistic pendulum from a ramp, and what factors (such as the elasticity of the collision, or friction) affect it?

• No. Volume doesn't matter. Mass and velocity are the primary factors. – Bill N May 27 '18 at 12:54
• In terms of the experiment, does it not even matter that the friction is proportionally less? – Eames May 27 '18 at 13:53
• 1) Momentum is conserved. 2)Friction doesn't depend on volume. 3) The amount of friction only affects the time interval for the ball velocity to match the pendulum velocity. 4) If the ball is moving with the pendulum, the collision is inelastic. 5) Volume by iteself has practically nothing to do with amount of momentum . It might affect the rate of transfer if the objects are not rigid. – Bill N May 28 '18 at 3:19