Crate Pushed up an Incline problem

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A crate weighing 27 kg is pushed up a ramp with a coefficient of kinetic friction of 0.24, and the problem involves calculating the work done by a person over a distance of 30 m at constant velocity. The forces acting on the crate include gravitational force and friction, which must be balanced for uniform motion. The solution involves summing the gravitational component along the ramp and the frictional force, then multiplying by the distance to find the total work done. Clarifications were provided on how to approach the calculations, emphasizing the need to account for both forces. The discussion concludes with a confirmation that the guidance was helpful in solving the problem.
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Homework Statement


A crate of mass 27 kg is pushed up a ramp by a person, as shown in the figure below. Assume the coefficient of kinetic friction between the crate and the ramp is .24. Calculate the work done by the person in pushing the crate a distance of 30 m as measured along the ramp. Assume that the crate moves with at a constant velocity.

Homework Equations


The Attempt at a Solution


I've tried a few different ways and I know something is missing but I can't quite figure out what. Here's what I've tried.

1. (27kg)(9.8)(sin30)=

2. (.24µk)(27kg)(9.8)(cos30)=

3. (.24µk(27kg)(cos30)(30m)=
 
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Hi Manda 24, welcome to PF.

The cart will move with uniform velocity when it overcomes the forces given by 1. and 2. in your attempt.
To find the work done, add 1 and 2 and multiply by the displacement.
 
Thanks, that helped.
 

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