Impulse

[MedPR]

Consider two tennis balls. When dropped from shoulder height, ball 1 hits the floor and rebounds to 80% of its original drop height. When dropped from shoulder height, ball 2 hits the floor and stops. In the collision with the floor, which ball receives the greater impulse?

A: Ball 1, because the impulse is about double that received by ball 2
B. Ball 1, because the impulse received by ball 2 is about zero
C. Ball 2, because the impulse received by ball 1 is about zero
D. Ball 2, because the time of interaction at the floor is very small

I thought that impulse=FdeltaT, so if the time of the collision is longer, the impulse is higher? Since ball 2 sticks to the ground, isn't it's T larger than Ball 1?

Also, how do you know that Ball 1's impulse is double that of Ball 2?

---

Members don't see this ad.

 

[Pisiform]

Impulse is just a change in momentum ... so lets suppose that both ball weigh 1 kg and both star at 1m/s, one ball would come to rest after collision vf = 0 .... while the other will rebound and would have some velocity (less than the original velocity of course) of lets say -0.8m/s (a guess)

So for second ball ... p_initial = 1 kgm/s ... p_final = 0 ... so change in momentum = impulse = -1kgm/s

for first ball ... p_initial = 1kgm/s ...p_final = 1*-0.8 = -0.8kgm/s ... so momentum change/impulse = -1.8kgm/s

so this will help you see how the first ball has a larger impulse than the second ball. Now between A & B ... you can eliminate B.

And yes even though the time of collision is longer ... the force would be less so impulse wont increase that much. Imagine, if you have played cricket or baseball, if you catch ball with a stagnant hand, you feel a lot of force on your hand (time is less) ... as compared to when you catch the ball while moving your hand in the direction of the ball (time of contact is more ... so force is less).

And also ... Impulse is change in momentum so we take the difference of momentum before collision and momentum after collision..

 

[MedPR]

Impulse is just a change in momentum ... so lets suppose that both ball weigh 1 kg and both star at 1m/s, one ball would come to rest after collision vf = 0 .... while the other will rebound and would have some velocity (less than the original velocity of course) of lets say -0.8m/s (a guess)

So for second ball ... p_initial = 1 kgm/s ... p_final = 0 ... so change in momentum = impulse = -1kgm/s

for first ball ... p_initial = 1kgm/s ...p_final = 1*-0.8 = -0.8kgm/s ... so momentum change/impulse = -1.8kgm/s

so this will help you see how the first ball has a larger impulse than the second ball. Now between A & B ... you can eliminate B.

And yes even though the time of collision is longer ... the force would be less so impulse wont increase that much. Imagine, if you have played cricket or baseball, if you catch ball with a stagnant hand, you feel a lot of force on your hand (time is less) ... as compared to when you catch the ball while moving your hand in the direction of the ball (time of contact is more ... so force is less).

And also ... Impulse is change in momentum so we take the difference of momentum before collision and momentum after collision..

Ok, I understand everything (thank you ) except for why the force would be less.

Isn't the force just ma? And if both balls are tennis balls, they have the same mass, and gravity is the same for both. Why don't they hit the ground with the same force?

 

[Pisiform]

Ok, I understand everything (thank you ) except for why the force would be less.

Isn't the force just ma? And if both balls are tennis balls, they have the same mass, and gravity is the same for both. Why don't they hit the ground with the same force?

hmm well the idea I learnt was specifically while catching the ball, but I think you can also apply here. When both ball touch the ground (at that very instant) both come at rest momentarily (one ball then rebounces while the other dies) so Impulse for both balls remain constant (at that instant) and to balance both sides, greater time of contact will cause less force. However this is not the momentum AFTER collision ... it is kinda during collision ...

 

[MedPR]

hmm well the idea I learnt was specifically while catching the ball, but I think you can also apply here. When both ball touch the ground (at that very instant) both come at rest momentarily (one ball then rebounces while the other dies) so Impulse for both balls remain constant (at that instant) and to balance both sides, greater time of contact will cause less force. However this is not the momentum AFTER collision ... it is kinda during collision ...

Oh ok, I think I understand. Thank you.