How Does h2 Compare to h1 for a Leaking Sand Cart?

[atarr3]

Homework Statement

A cart containing sand starts at rest and then rolls, without energy loss to friction, down into a valley and then up on a hill on the other side. The initial height is h1 and the final height is h2. If the cart leaks sand along the way, how does h2 compare to h1?

Homework Equations

$$V(x) = mgx$$ and $$K = \frac{1}{2}mv^{2}$$

The Attempt at a Solution

I am a little confused about what this problem is asking for. Are they just looking for whether or not h2 is lower or higher than h1 and then just prove it? And if so, I'm not really sure how to prove that. I know that the cart is losing energy because the sand flying out represents the kinetic energy of the system, so I feel like h2 would be lower than h1 as a result. But I don't know how to show this if this is the correct answer.

 

[willem2]

compare the acceleration of the cart with that of a similar cart that doesn't leak.