work and power problem?

Question

A 109kg crate is pulled along a level surface by an engine. The coefficient of kinetic friction between the crate and the surface is 0.28. The acceleration for gravity is 9.8m/s^2 how much power must the engine deliver to move the crate at a constant speed of 4.04m/s. answer in units of watts. also, how much work is done by the engine in 3.64 minutes.

I have no idea how to do this....

Answer 1

First look at the forces on the crate. Our coordinate system will be +x to the right and +y up.

Gravity, mg, in the -y direction (down)
Normal force, N, in the +y direction (up)
P, the pulling force, in the +x direction (right)
uN, the friction force (where u is the coefficient of friction), in the -x direction (left)

Apply Newton's Second Law in the vertical dimension. There's no net force, so F = ma = 0

N - mg = 0 so N = mg

Now use Newton's Second Law in the horizontal direction. Again, there's no acceleration (constant velocity) so

P - uN = 0 so P = uN = umg

Work is force multiplied by distance. The crate is moving at 4.04 m/s, so the work done by friction each second is

Force of friction * distance moved in one second
( umg ) (4.04 m)

You now have the work per second, which is the power provided by the engine.

To find the work done in 3.64 minutes, you need to find out how far the box moves during that time. That distance is simply velocity * time or ( 4.04 m/s ) ( 3.64 min ) ( 60 sec / min ). Now multiply that time by the friction force, uN, to get the work done over that distance.