Work done by a constant force problem

[mooney82]

Homework Statement

A 1.8kg block is moved at constant speed over a surface for which uk = 0.25. The displacement is 2 m. It is pushed with a force at 45 degrees below the horizontal.
Find the work done by: (a) the force F; (b) friction; (c) gravity

Homework Equations

W=Fs cos (theta)

s=displacement

The Attempt at a Solution

First I found the force F to be 6.24 N.

Then using W=Fs cos (theta) I put in:

W=6.24 N * 2 m * cos 135
W= -8.82

The answer in the back of the book says 11.8, I'm wondering where I'm making my mistake.

 

[Doc Al]

First I found the force F to be 6.24 N.

How did you solve for the force?

Then using W=Fs cos (theta) I put in:

W=6.24 N * 2 m * cos 135

Why did you use an angle of 135? (That's why your answer is negative.) But first figure out the force properly.

 

[mooney82]

Well, I summed the x component forces:
Fcos45 - friction = ma

acceleration = 0
friction = uk(N)
N equals mg

so

Fcos45 - uk(mg)=0

F = uk(mg)/cos45

F = 0.25*1.8*9.81/cos45

 

[Doc Al]

N equals mg

Here's the problem. In this case, N ≠ mg. The fact that the applied force has a vertical component changes the normal force.

To find the normal force, analyze the vertical components of the forces acting on the block.

 

[mooney82]

Here's the problem. In this case, N ≠ mg. The fact that the applied force has a vertical component changes the normal force.

To find the normal force, analyze the vertical components of the forces acting on the block.

Would you then solve by substitution? I'm having a hard time because F seems to cancel out.

 

[Doc Al]

Would you then solve by substitution?

Yes. You'll have two equations: one for vertical forces; one for horizontal. You can eliminate N by substituting one into the other.

I'm having a hard time because F seems to cancel out.

Show what you're doing.

 

[mooney82]

Yes. You'll have two equations: one for vertical forces; one for horizontal. You can eliminate N by substituting one into the other.

Show what you're doing.

I got it to work out. You tha man Al!