Question

So here is an interesting question which I have tried to explain. It would be great if any one can verify it. Thanks

Answer 1

The question is about elastic collision. A ball of mass m is travelling with a velocity v. It collides with a wall and bounces back with same velocity. Change in momentum is 2mv and since no external force is applied this momentum must be imparted by wall. But the velocity of wall is zero.
\(\bf \text{Can a body posses momentum without any kinetic energy.} \\ \text{Is it mathematically correct?}\)

Answer 2

So, the most common reason I could figure out is that yes the wall has a momentum but has almost zero K.E because the mass of wall is infinite (in comparison to ball, that's why it bounced back with same speed in first place). Mathematically speaking,

\(\sf \Large K.E=\frac{P^2}{2m}\). Since, m=\(\infty\), K.E will be zero.

Answer 3

The momentum (p) of photon which has zero rest mass of electromagnetic radiation with wavelength λ is,
p = h/λ
Since the photon has zero rest mass therefore the kinetic energy of the photon is zero, but still the photon has momentum. Therefore a body has a momentum without having kinetic energy.

Answer 4

I don't think it's appropriate to draw an analogy with the photon in this situation. yeah, it's ok that the photon has a mometum and don't have a mass, but the main thing is that all general laws of physics work with photons. The laws of conservation of energy and momentum. Although here we have a different thing - a wall, a body with an infinite mass. And I suppose that the Abhizar's explanation is correct (we should also add that the wall is rigid).
P.S. In reality the mass of a wall is not infinite of course, but it doesn't mean that we break any laws. The wall is deformated by the ball and then this wall K.E. quickly transform to heat energy

Answer 5

Thanks Andrey, and yes you are correct. in reality the wall does deform a bit.

Answer 6

Got it.... Not to add Chemistry in Physics

Answer 7

why would you say that the mass of the wall is infinite?

Answer 8

Because after collision is returning back with same speed. Now if you are familiar with head on collisions then you know that it is only possible when one of the masses is >> than the other. @panlac01

Answer 9

yeah, it's just a mathematical approximation to explain why the wall is motionless. (without saying it we should have said about the transformation of K.E. to heat energy. So it's easier to say that the wall has infinite mass)

Answer 10

I was hoping you would show us mathematically

Answer 11

as Abhisar said:
K.E=P^2/(2m). Since, m=∞, K.E will be zero.