If a box is given a shove so it slides up an incline then slides back down to its starting point, will it take longer on the way up or on the way down? I think it's down.

Assuming friction or not?

No and yes. If no, I'm assuming it takes the same time to go up and down? But with friction... hmmmmm.

It seems to me that it would be equal because the force applied to push it up the incline will only serve to make it go further up and gradually slow until it gets as far as it will go, then on the way down it will begin slowly and pick up speed as it goes. The force applied to overcome gravity on the way up is then absent on the way down.

Imagine a ball thrown straight up in the air. When it gets to the highest point, it would then take the same amount of time to get back to where it started.

I'd love to hear other thoughts on my logic.

Friction would be constant going up or down.

I think it takes longer on the way down, assuming friction is present. When going up there are two components of forces opposing its motion - both gravity and friction are causing it to slow,so ut will slow pretty quickly. But on the way down gravity is causing it to accelerate while friction is causing it to go slower. Hence the sum of the forces when going up is a greater opposing force than the sum of the forces on the way down. This means that the deceleration on the way up is greater than the acceleration on the way down.

You can see this perhaps clearer if you think through a couple of examples. The example that OneGuy described is correct if there is no friction present. But imagine the case where the friction force is equal to or greater than the gravity force - in this case after the object moves up the ramp and stops, it never stars sliding back down, so here the time it takes to slide down is infinite. Thus as long as riction is present, it takes longer to go back down the ramp than it took to go up and come to a stop.

Wowwww, this stuff makes total sense now! Thanks people!