Solve the Homework Problem with Work and Energy

[Anthonyphy2013]

Homework Statement

Doug pushes a 5.30 kg crate up a 2.20-m-high 20 degrees frictionless slope by pushing it with a constant horizontal force of 27.0 N. What is the speed of the crate as it reaches the top of the slope?

a) Solve this problem using work and energy.

Homework Equations

Wd=delta KE, ke=.5mv^2 and pe=mgh

The Attempt at a Solution

Conservation of energy
W.d=Pe+KE
Fcos20=mg(h/sin20)+.5mv^2
v= 3.9m/s
but I consider another way about the work done
work done = delta KE
work done on force = Fcos20
work done against the gravitational force = mg(h/sin20)
so Work done by force - work done against the gravitational force =Change of KE .
which one is a corrected concept or both make sense. thanks so much.

 

[szynkasz]

...Fcos20=mg(h/sin20)+.5mv^2...

This is not correct.

 

[Anthonyphy2013]

This is not correct.

why is that not corrected ?
Since work done must be equal to delta KE , so we consider workd done on gravitational force is not a conserved work done ?

 

[szynkasz]

Left side of the equation is force, right is energy. Potential energy is $mgh$, not $mg\frac{h}{\sin 20^o}$