A horizontal force of magnitude F = 176.0 N is used to push a box of mass m = 9.0 kg from rest a distance d = 15.0 m up a frictionless incline with a slope θ = 31.0°.

1) How much work is done by the force on the box?

W F =

To find the work done by the force, use the formula:

W = F * d * cos(θ)

where:
W is the work done
F is the magnitude of the force
d is the distance
θ is the angle between the force and the direction of motion.

In this case, the angle θ is 31.0°, the force magnitude F is 176.0 N, and the distance d is 15.0 m.

Plugging these values into the formula, we get:

W = 176.0 N * 15.0 m * cos(31.0°)
W = (176.0 N * 15.0 m) * cos(31.0°)

Now, multiply 176.0 N by 15.0 m to get the product of (176.0 N * 15.0 m):

W = 2640.0 N*m * cos(31.0°)

Finally, find the cosine of 31.0° on your calculator and multiply it by 2640.0 N*m:

W = 2640.0 N*m * cos(31.0°)
W ≈ 2278.5 J

Therefore, the work done by the force on the box is approximately 2278.5 Joules.