Energy & Momentum Thinking Problem

[Nicolaus]

Homework Statement

Two boxes each of mass 12kg are raised 1.8m to a shelf. The first one is lifted and the second is pushed up a smooth ramp. If the applied force on the second box is 48N, calculate the angle between the ramp and the ground.

Homework Equations

W = Eg = mgh for first (lifted) box
Trig to calculate angle

The Attempt at a Solution

I first calculated the gravitational energy on the first box that is lifted:
Eg = (12kg)(9.8m/s^2)(1.8m) = 211.7N
Then, knowing that, used trig to calculate the angle between ramp and ground:
Sin (theta) = opposite (211.7N)/hypoteneuse(48N)
and, naturally, this does not compute, so where did I go wrong?

 

[Doc Al]

I first calculated the gravitational energy on the first box that is lifted:
Eg = (12kg)(9.8m/s^2)(1.8m) = 211.7N

That's an energy, not a force. Its units are Joules, not Newtons.

Then, knowing that, used trig to calculate the angle between ramp and ground:
Sin (theta) = opposite (211.7N)/hypoteneuse(48N)
and, naturally, this does not compute, so where did I go wrong?

Not sure what you are trying to do. Instead, examine the forces acting on the box as it is pushed up the ramp. (Assume the force applied is just enough to slide it up the ramp.)

Hint: What's the component of the box's weight parallel to the ramp?

 

[Nicolaus]

Whoops, it's been a while. Anyways, I got:
Fnet = Fa - Fg(parallel)
= 48N - (12)(8.8)sin(angle)
= 48N - 117.6Nsin(a)
sin(a) = 48/117.6
angle = 24.1 degrees?

 

[Doc Al]

Whoops, it's been a while. Anyways, I got:
Fnet = Fa - Fg(parallel)
= 48N - (12)(8.8)sin(angle)
= 48N - 117.6Nsin(a)
sin(a) = 48/117.6
angle = 24.1 degrees?

Good!