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 $mg\frac{h}{\sin 20^o}$

 

[Nickie]

Both concepts make sense and can be used to solve the problem. The first concept uses the conservation of energy principle, where the work done by the force pushing the crate up the slope is equal to the change in potential energy (due to the change in height) plus the change in kinetic energy (since the crate starts from rest at the bottom of the slope). This results in the equation Wd=Pe+KE, which can be rearranged to solve for the final speed of the crate.

The second concept involves breaking down the work done into the work done by the applied force and the work done against the gravitational force. This results in the equation Work done by force - work done against the gravitational force =Change in KE. This approach can also be used to solve for the final speed of the crate.

Both approaches are valid and can be used to solve the problem. It is important to understand the underlying principles of work and energy and how they can be applied in different ways to solve problems.