Question - Work Done by a Force at an Angle

The work done by a force when the force is applied at an angle to the direction of displacement can be calculated using the formula:

\( W = F \cdot d \cdot \cos(\theta) \)

where:

\( W \) is the work done,

\( F \) is the magnitude of the force,

\( d \) is the displacement,

\( \theta \) is the angle between the force and the displacement.

Given that \( F = 50 \) N, \( d = 10 \) m, and \( \theta = 30^\circ \), the work done \( W \) is

\( W = 50 \cdot 10 \cdot \cos(30^\circ) \)

\( W = 500 \cdot \frac{\sqrt{3}}{2} \)

\( W = 250\sqrt{3} \) J

Therefore, \( 250\sqrt{3} \) joules of work is done by the force.