# Question about mechanical energy in an isolated system

1. Oct 27, 2008

### fluidistic

Hello,
Consider a system that is made of a man and a hockey ball on ice (frictionless).
Say the man's mass is 80kg and the ball is 0.5kg.
At $$t=0$$, they are together and they don't move. At an instant the man throw the ball at $$\frac{10m}{s}$$ against a wall (the ball suffers an elastic collision) and finally reaches the man. If the man repeat this experience again and again he will get a velocity each time greater, but it doesn't double at each time. In fact I've thought about it and he would eventually reach a velocity close to $$\frac{10m}{s}$$ (I think it's possible for him to reach a velocity even a bit greater, but then the ball wouldn't be able to reach the man so the velocity of the man would then be definitive).
My question is : What is the total mechanical energy of the system? I think we have to separate it into the one from the man and the one from the ball. As the ball is always moving with a speed of $$\frac{10m}{s}$$, I think it remains unchanged. ($$E=\frac{mv^2}{2}$$). While the mechanical energy of the man is growing up! (Since his speed is increasing each time he hits the ball). So my guess is that the mechanical energy of the man is not equal to $$\frac{mv^2}{2}$$, in other words he must have a potential energy. How can I find it out? Remember that it is possible for the man to get over $$\frac{10m}{s}$$.
Thanks!

2. Oct 27, 2008

### Staff: Mentor

I don't really understand the question. Several points: Is the ball thrown at 10 m/s with respect to the man? Then, as the man's speed increases, the speed of the thrown ball with respect to the ground will decrease. The man's mechanical energy increases--he speeds up. But the man is not a point mass, he has internal mechanisms that convert chemical energy (from food and oxygen) into mechanical energy.

3. Oct 27, 2008

### fluidistic

Oops sorry, yes it is thrown at 10m/s with respect to the man... I forgot that the speed of the ball would decrease with respect to the ground.
But the point is that I didn't know I couldn't consider the man as a simple body. So the potential energy of the man comes from his food/water/oxygen. This explains it all.
Thank you Doc Al!