Work done by a constant force problem

AI Thread Summary
A 1.8 kg block is pushed at a constant speed over a surface with a coefficient of friction of 0.25, and the displacement is 2 m. The force applied at a 45-degree angle below the horizontal was initially calculated as 6.24 N, but the work done was incorrectly computed due to using the wrong angle in the work formula. The normal force is affected by the vertical component of the applied force, necessitating a reevaluation of the forces acting on the block. To find the correct normal force, one must analyze both vertical and horizontal components of the forces. The discussion concludes with a successful resolution of the problem after clarifying the calculations.
mooney82
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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.
 
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mooney82 said:
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.
 
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
 
mooney82 said:
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.
 
Doc Al said:
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.
 
mooney82 said:
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.
 
Doc Al said:
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!
 

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