Forces...Work Done...Find Angle?

Question

I'm confused about this problem. Can anyone help me with it? Thx!

A force F with the magnitude 250 lb moves an object in the direction of the vector D a distance of 20 ft. If the work done is 3800 ft-lb, find the angle between F and D.

Answer 1

This problem has 2 steps:

Step 1: Find the work done along vector D:
W = Fd
The work done along vector D is 250 lb * 20 ft = 1000 ft-lb

Step 2: Find the angle by imagining a triangle:
If we drew a triangle, where the F goes along the hypotenuse, and D is our vector, then cos Θ would equal the adjacent vector (D) over the Force (F).

cos Θ = 1000 ft-lb / 3800 ft-lb = 1/3.8 = 0.263
Θ = 74.74 degrees.