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!

 

[Nickie]

As a scientist, it is important to carefully consider all the given information and equations before attempting to solve the problem. In this case, the equation W = Eg = mgh is only applicable for the first box that is lifted. For the second box, which is pushed up the ramp, the equation for work done is W = Fd, where F is the applied force and d is the displacement along the ramp.

Therefore, to solve for the angle between the ramp and ground, we can use the equation W = Fd, where W is equal to the gravitational energy of the second box, which is also equal to the work done by the applied force. So we can set up the equation as follows:

W = Fd = mgh
48N (distance along ramp) = (12kg)(9.8m/s^2)(1.8m)
d = 1.8m

Now, using trigonometry, we can calculate the angle between the ramp and ground:

Sin (theta) = opposite (1.8m)/hypotenuse (distance along ramp)
Sin (theta) = 1.8m/d
Sin (theta) = 1.8m/1.8m
Sin (theta) = 1
theta = sin^-1(1)
theta = 90 degrees

Therefore, the angle between the ramp and ground is 90 degrees. This makes sense because the box is being pushed up a smooth ramp, so the normal force from the ramp would be perpendicular to the ground and the angle between the ramp and ground would be 90 degrees.