What are the effects of impulse and kinetic energy on two identical spheres?

[cheapstrike]

Homework Statement

Two identical spheres A and B are kept on a smooth surface. They are given the same impulse I. The lines of action of impulses pass through the center of A and away from the center of B. Then:

(A) linear kinetic energy of B will be less than that of A. (B) B will have greater kinetic energy than A.
(C) A and B will have the same kinetic energy. (D) none of the above.

2. The attempt at a solution

Sorry I didn't go by the template because I didn't know how to begin the problem.

I cannot actually visualize how the impulses will be acting on the two spheres. It is given that the line of action of Impulse passes through the center of A. Ok, I got it. But away from the center of B? Shouldn't that also not pass through the center?

 

[oz93666]

check you have posted the question exactly, word for word ...is there an impulse or impulses?

 

[cheapstrike]

check you have posted the question exactly, word for word ...is there an impulse or impulses?

Yup.. I checked the question. What I think is that A and B are given an impulse I each and the point of application is different in each case. Much like saying that a sphere in one case is given I at one point and in another case at another point, both cases being completely independent.

 

[PeroK]

Yup.. I checked the question. What I think is that A and B are given an impulse I each and the point of application is different in each case. Much like saying that a sphere in one case is given I at one point and in another case at another point, both cases being completely independent.

Imagine striking two snooker balls with a cue. A is struck in the middle, B is struck to one side, which not only propels B but imparts spin as well.

 

[cheapstrike]

Imagine striking two snooker balls with a cue. A is struck in the middle, B is struck to one side, which not only propels B but imparts spin as well.

Ok.. so the perpendicular distance of Impulse on A and B from the center will be 0 and R (or 0<d≤R) respectively?

 

[PeroK]

Ok.. so the perpendicular distance of Impulse on A and B from the center will be 0 and R (or 0<d≤R) respectively?

I guess you mean $d < R$?

You don't really need any equations here. There is a quick way to see the answer. But, the explanation of why the same impulse can produce more energy is hard to see, I always think.

 

[cheapstrike]

I guess you mean $d < R$?

You don't really need any equations here. There is a quick way to see the answer. But, the explanation of why the same impulse can produce more energy is hard to see, I always think.

Yeah.. I was just quantifying what you said earlier so as to double check if I am thinking correctly. Thanks again.

 

[Abhayahuja]

Will the velocities of COM of A and B be equal? If yes, then why? If not, then how do we compare the final K.E. of the two spheres?

 

[PeroK]

Will the velocities of COM of A and B be equal? If yes, then why? If not, then how do we compare the final K.E. of the two spheres?

Yes, by definition of impulse, which is force by time and represents a change in linear momentum. Given the same impulse the linear momentum of A and B must be the same.

 

[Abhayahuja]

Ok

Yes, by definition of impulse, which is force by time and represents a change in linear momentum. Given the same impulse the linear momentum of A and B must be the same.

As the linear K.E. of both blocks is same and block B has some rotational K.E., therefore net K.E. of B will be greater, right?

 

[PeroK]

Ok

As the linear K.E. of both blocks is same and block B has done rotational K.E., therefore net K.E. of B will be greater, right?

Yes, B also receives a torque (because the impulse is not directed through its COM), so gets rotational momentum (and KE) in addition to its linear momentum (and linear KE).

The tricky question, in my opinion at least, is how the same force in the same time can impart more energy in one case than the other?

Hint: do not think of the impulse as being "instantaneously" delivered, or delivered in an "infinitesimal time".

 

[Abhayahuja]

Well, ur last statement just created a new doubt. Sorry but I didn't get the hint.

 

[PeroK]

Well, ur last statement just created a new doubt. Sorry but I didn't get the hint.

If the impulse is instantaneous then it is over zero distance.