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## Homework Statement

Suppose a worker pushes down at an angle of 30° below the horizontal on a 30.0‐kg crate

sliding with along a horizontal warehouse floor (μ[tex]_{k}[/tex] = 0.25) for 4.5 meters.

a. What magnitude of force must the worker apply to move the crate at constant velocity?

b. How much work is done on the crate by this force over the 4.5 m?

c. How much work is done on the crate by friction over that same distance?

d. How much work is done on the crate by the normal force over this distance?

e. How much work is done on the crate by gravity?

f. What is the total work done on the crate?

## Homework Equations

W = F[tex]_{par}[/tex]d

## The Attempt at a Solution

(d), (e), and (f) are pretty simple. The normal force and gravity are perpendicular to motion so don't affect work. Since it's moving at a constant velocity, the net force is zero, so there's no work there either.

My problem is really the distinction between (b) and (c). I calculated the frictional force to 73.5 N. For part (a), the frictional force is just the horizontal component of the total force needed to push the crate. But only the frictional force will affect the amount of work done, right? So (b), and (c) are the same answer?