What speed should you push the box

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AI Thread Summary
To determine the speed at which to push the box of nails down a 23-degree roof, one must consider the forces acting on the box, including gravity and friction. The coefficient of kinetic friction is 0.50, which will affect the box's motion as it slides down the roof. The initial kinetic energy must equal the work done against friction plus the change in potential energy as the box moves down the slope. By applying energy conservation principles, the required initial speed can be calculated to ensure the box comes to rest at the edge of the roof. Understanding these dynamics is crucial for solving the problem effectively.
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Homework Statement



You and your friend Peter are putting new shingles on a roof pitched at 23degree . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4 m away, asks you for the box of nails. Rather than carry the 2.3 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him.
If the coefficient of kinetic friction between the box and the roof is 0.50, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Homework Equations


I don't know lol



The Attempt at a Solution


so I drew the free body diagram but I really don't know where to go from there. I think the problem is i just don't know which equations to use. any help is appreciated
 
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Use energies. It starts out with energy that carries it down the roof and stops at the bottom with zero final energy. There was work down on it to change the energy, frictional work.

W = Delta KE
 
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