# Work done (1)

1. Jul 14, 2013

### Anthonyphy2013

1. The problem statement, all variables and given/known data

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.

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

3. 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.

2. Jul 14, 2013

### szynkasz

This is not correct.

3. Jul 14, 2013

### Anthonyphy2013

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 ?

Last edited: Jul 14, 2013
4. Jul 16, 2013

### szynkasz

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