Answer to Question #331234 in Physics for Sam

Question

You pull a box using a rope, which is directed 30 degrees above the horizontal. You apply a constant force of 30 N, and you move the box 5 m along the ground. What work did you do in Joules?

Answer 1

By definition, the work is the scalar product of the force and displacement:

$$W = \mathbf{F}\cdot \mathbf{d}$$

Since the box is displaced along the horizontal direction, and the force makes $\theta=30\degree$ with horizontal, the formula for the scalar product becomes:

$$W = Fd\cos\theta$$

where $F = 30N, d = 5m$. Thus, obtain:

$$W = 30N\cdot 5m\cdot \cos30\degree \approx 130J$$

Answer. 130 J.