How much work is done on a crate pushed along an incline with constant velocity?

[thephysicslife]

Homework Statement

40 kg crate is pushed at a constant velocity along an incline with a vertical height of 4 m and inclined distance of 7 m. How much work was done on the crate in moving it to the top of the ramp?
For the incline, think of a right angle triangle with the 7 m being the hypotenuse.

Homework Equations

W=m|g|h
W=|fa||d|
W=m*a*d
W=1/2mv²
Any dynamic equations ( I don't think they are necessary for this question though)

The Attempt at a Solution

W=Ep
=m*|g|*H
=40kg*9.81m/s²*4m
=1.3x10² J

The thing I am unsure about is if the velocity is constant, does that mean the formula would be W=1/2mv² and the answer would be 0 Joules because the velocity is constant? Would be find the angle of the incline using sine?

 

[gneill]

The Attempt at a Solution

W=Ep
=m*|g|*H
=40kg*9.81m/s2*4m
=1.3x102 J

Check your arithmetic.

The thing I am unsure about is if the velocity is constant, does that mean the formula would be W=1/2mv2 and the answer would be 0 Joules because the velocity is constant? Would be find the angle of the incline using sine?

That would give you the kinetic energy of the crate, if you happened to know the velocity. But you were not given the velocity. Just because a value is constant doesn't mean you can make it zero.

You have two choices here. You can calculate the change in gravitational PE as you (nearly) did above, or you can determine the force required to push the crate at a constant velocity (what force must the push counteract?). Then use the usual work formula involving force and distance.

You can use trigonometry to find the angle if you think you need it. The sine and cosine of it can be determined directly by suitable ratios of the triangle sides.[/quote]