Balls moving against each other

Question

Ball made of steel and ball made of aluminum move against each other, one time both with 4 m/s, another time both with 2 m/s. Compare the ratio of accelerations and explain your answer.

Answer 1

Hi Gabrielius T.,

Some information is missing in this question of yours. It's interesting that the balls have different composition, I guess. But what exactly were the physical circumstances (are the balls solid, hollow, the same size, mass etc.) and circumstances of the "moving against"? Is this a head-on collision on a horizontal plane, or are they rolling in the same direction, approximately, and just rubbing up?

Assuming you can muster some of those bits of data, then you can start doing dynamics. Collisions take place with conservation of the movement of the center-of-mass of the system. In that frame of reference, each ball approaches the other to a stationary, "spring-loaded" condition, and rebounds. The distance over which the total interaction takes place (in and out) will depend on the relative masses of the balls (to determine the trajectory of the CM) as well as their elastic deformation constants. There is no guarantee that the stress vs. strain is linear; but if it were, the time to load and unload the "spring" of each ball would be similar to that of an oscillating mass on a spring (simple harmonic motion), which you have probably studied?

-- Cheers, --Mr. d.