Solving Friction & Skier Homework with Work-Energy Theorem

[xgoddess210]

Homework Statement

You are a member of an alpine rescue team and must get a box of supplies, with mass 2.20 kg, up an incline of constant slope angle 30.0 degrees so that it reaches a stranded skier who is a vertical distance 2.80 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10^−2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s^2.

Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.

Homework Equations

W= kf-ki+ uf-ui

The Attempt at a Solution

I don't really see how the work-energy theorem applies. I know we have the kinetic coefficient of friction, but what about the potential. I'm very confused by this problem!

 

[G01]

The work-energy theorem does indeed apply. You are going to need to show some work before I can help you much. Try starting by answering these questions:

1. Can you state the work-energy theorem?

2. What force is doing the work?

 

[xgoddess210]

ok. The work energy theorem is basically saying that since energy is always conserved, something had to provide energy and its done through work. So in less words it is the relationship between the work done and the change in energy.

I think gravity is doing most of the work by pulling the box down, but i don't really know.

Also, what exactly does the question mean? A person is pushing a box up an incline that they can't walk up, so I have to find how hard it would have to be pushed to get it all the way up the slope, even with friction and gravity pulling it back down?

 

[LowlyPion]

ok. The work energy theorem is basically saying that since energy is always conserved, something had to provide energy and its done through work. So in less words it is the relationship between the work done and the change in energy.

I think gravity is doing most of the work by pulling the box down, but i don't really know.

Also, what exactly does the question mean? A person is pushing a box up an incline that they can't walk up, so I have to find how hard it would have to be pushed to get it all the way up the slope, even with friction and gravity pulling it back down?

If you know how high vertically it has to go that gives you the Potential energy that it needs at a minimum doesn't it?

And you also should be able to figure how much work needs to be done against friction over the length of the slope.

So if work needs to be done to overcome friction how would that enter into your thinking about the kinetic energy you need to impart at the bottom?