Rubber ball colliding with steel ball of equal mass

[goraemon]

Homework Statement

Suppose a rubber ball collides head-on with a steel ball of equal mass traveling in the opposite direction with equal speed. Which ball, if either, receives the larger impulse? Explain.

Homework Equations

p = m*v
impulse force = change in p

The Attempt at a Solution

(1) At first I intuitively thought that since the rubber ball is more "bouncy" than the steel ball, it'll likely bounce off after the collision and travel in the opposite direction at a greater speed than the steel ball will. So I thought that the rubber ball will have larger change in momentum, and thus will exert more impulse, meaning the steel ball will receive the larger impulse.

(2) But then, I began thinking that my intuition may not be correct. The momentum change must be the same for both balls regardless of whether they're steel or rubber, meaning the impulse force must be equal...also, impulse is nothing more than the integral of the force exerted during some time interval. The balls collide for the exact same time interval, and the force exerted by the balls on each other is also the same.

Is answer (2) correct? If so, would the answer remain the same if the question were changed to the following: "Suppose a rubber ball collides head-on with a steel ball of equal mass traveling in the opposite direction with **DIFFERENT** speeds."

Thanks a lot.

 

[SammyS]

Homework Statement

Suppose a rubber ball collides head-on with a steel ball of equal mass traveling in the opposite direction with equal speed. Which ball, if either, receives the larger impulse? Explain.

Homework Equations

p = m*v
impulse force = change in p

The Attempt at a Solution

(1) At first I intuitively thought that since the rubber ball is more "bouncy" than the steel ball, it'll likely bounce off after the collision and travel in the opposite direction at a greater speed than the steel ball will. So I thought that the rubber ball will have larger change in momentum, and thus will exert more impulse, meaning the steel ball will receive the larger impulse.

(2) But then, I began thinking that my intuition may not be correct. The momentum change must be the same for both balls regardless of whether they're steel or rubber, meaning the impulse force must be equal...also, impulse is nothing more than the integral of the force exerted during some time interval. The balls collide for the exact same time interval, and the force exerted by the balls on each other is also the same.

Is answer (2) correct? If so, would the answer remain the same if the question were changed to the following: "Suppose a rubber ball collides head-on with a steel ball of equal mass traveling in the opposite direction with **DIFFERENT** speeds."

Thanks a lot.

The second version is a very good analysis, especially the use of Newton's 3rd Law.


For the second scenario, ... how would your previous answer have to be modified? -- if at all ?

 

[goraemon]

The second version is a very good analysis, especially the use of Newton's 3rd Law.


For the second scenario, ... how would your previous answer have to be modified? -- if at all ?

Thank you for your response SammyS. My guess is that the answer should not change for the second scenario (where the balls' initial speeds are different), since the force exerted by the balls on each other should be the same in magnitude regardless of whether their initial speeds are the same or different...and the time interval of the force should also remain the same...is this reasoning correct or am I off base?

 

[SammyS]

Thank you for your response SammyS. My guess is that the answer should not change for the second scenario (where the balls' initial speeds are different), since the force exerted by the balls on each other should be the same in magnitude regardless of whether their initial speeds are the same or different...and the time interval of the force should also remain the same...is this reasoning correct or am I off base?

You are correct with that answer !

 

[HalfLostAndSearching]

Your second answer is correct. The impulse force is determined by the change in momentum, which is the same for both balls in this scenario. Therefore, the impulse force will be equal for both balls.

If the question were changed to have different speeds, the impulse force would still be equal as long as the masses and velocities are still equal. This is because the change in momentum is still the same, regardless of the initial velocities of the balls.

It is important to note that the materials of the balls (rubber vs steel) do not affect the impulse force in this scenario. The only factors that affect the impulse force are the masses and velocities of the balls.