Question

Trevor is pulling his younger brother in a wagon. He pulls the wagon 50 m to the corner with a force that is parallel with the ground. He then turns the wagon around and pulls it 50 m back to the starting point with the same force at an angle of 30° with respect to the ground.

How does the amount of work Trevor performs going to the corner compare with the amount of work he performs coming back?

They are the same because he uses the same amount of force.
They are the same because he travels the same distance.
He does less work coming back because the force moving the wagon is only 50cos30°.
He does more work coming back because the force moving the wagon is only 50cos60°.

Answer 1

He does less work coming back — third choice.

Reason: Work = F·d = F d cosθ. Going out θ = 0° so W1 = F(50)cos0 = 50F. Coming back θ = 30° so W2 = F(50)cos30 = 50F(cos30) ≈ 50F(0.866). Only the horizontal component does work, so W2 < W1 (about 86.6% of W1).