Using Work Energy Theorem to Find Necessary Velocity

[Thenotsophysicsguy]

1. The problem statement, all variables and given/
You must push a box up an incline plane (the angle being constant : a), to a person waiting to receive it, who is a distance of h(constant) vertically above you. Though the slope is slippery, there is a small amount of friction with kinetic friction coefficient μ_k. Use the work-energy theorem to determine the minimum speed at which you must push the box, so that it may reach the receiver. Express answer in terms of g, h, μ_k, and a

Homework Equations

Among many equations there are:
F_k=μ_k*F_n (F_N being natural force)
Force of Gravity=mg

The Attempt at a Solution

I know that the answer is the square root of 2gh(1+μ_k/tan(a)), but I am not fully sure what the steps are to reaching this conclusion.

 

[gneill]

What have you tried? What does the work-energy theorem say? What are the types of energy involved here?

 

[TomHart]

I thought the wording of this problem was a little vague. Just to clarify, the person at the bottom gives the box a shove, and releases it at an initial velocity such that the box slides up the incline (without any additional pushing) and just barely makes it to the top.

 

[Thenotsophysicsguy]

exactly