# Impulse and kinetic energy?

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1. Jan 4, 2017

### cheapstrike

1. The problem statement, all variables and given/known data

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?

2. Jan 4, 2017

### oz93666

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

3. Jan 4, 2017

### cheapstrike

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.

4. Jan 4, 2017

### PeroK

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.

5. Jan 4, 2017

### cheapstrike

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

6. Jan 4, 2017

### PeroK

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.

7. Jan 4, 2017

### cheapstrike

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

8. Jan 4, 2017

### 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?

9. Jan 4, 2017

### PeroK

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.

10. Jan 4, 2017

### Abhayahuja

Ok
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?

11. Jan 4, 2017

### PeroK

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".

12. Jan 4, 2017

### Abhayahuja

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

13. Jan 4, 2017

### PeroK

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