# Is kinetic energy always conserved in an elastic collision/impact?

While working out through some problems I encountered this problem :

A ball moving with a velocity $$v$$ hits a massive wall moving towards the ball with a velocity $$u$$. An elastic impact lasts for a time $$\Delta t$$

Now I have to answer whether the Kinetic energy of ball increases or remains same after collision.

In the theory books which I read, it is mentioned that Kinetic energy is conserved before and after in an elastic collision.

So that way for the above question Kinetic energy should be conserved.

But the answer given is that Kinetic energy increases.

So my question is how is it possible for Kinetic energy to increase after an elastic impact ? Is it because of the time interval $$\Delta t$$?

• Does the question specifically mention kinetic energy of the *ball only after collision? Because kinetic energy of the system remains unchanged after elastic collision but the kinetic energy of the individual objects will change depending on the mass of the objects but will remain balanced. Have you looked up the wiki article on this? – Rumplestillskin Aug 15 '19 at 6:40

## 2 Answers

In the theory books which I read, it is mentioned that Kinetic energy is conserved before and after in an elastic collision.

Yes, but keep in mind this is the total kinetic energy. i.e. it's the sum of kinetic energy of both the ball and the wall.

So my question is how is it possible for Kinetic energy to increase after an elastic impact ? Is it because of the time interval Δt?

The total kinetic energy is constant, by the definition of elastic collision. However, your question is asking about just the ball. If the ball's kinetic energy increases, then the wall's kinetic energy must decrease.

Therefore, it looks like your confusion lies in what is being talked about when. The question is talking about just the ball. When we talk about kinetic energy being conserved in elastic collisions, we are talking about the entire system.

While @Rumplestillskin has basically answered your question, here is an intuitive explanation. The total kinetic energy of the wall and the ball together is preserved after the ball bounces off. Now, since the wall was moving towards the ball, however small the ball is, it had slowed the wall a bit. So part of wall's energy has passed to the ball, thus ball's energy has increased. Imagine that the wall is actually a tennis racket - it is relatively massive, and hitting the incoming ball. Naturally, the ball returns faster than it came in when you hit it.