Question - Calculating Work Done by a Force at an Angle

The work \( W \) done by a force when moving an object through a displacement \( d \) at an angle \( \theta \) to the direction of the force is given by:

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

Given that the force \( F \) is \( 50 \text{N} \), the displacement \( d \) is \( 10 \text{m} \), and the angle \( \theta \) is \( 30^\circ \):

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

First, calculate \( \cos(30^\circ) \):

\[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \]

Then compute the work done \( W \):

\[ W = 50 \cdot 10 \cdot \frac{\sqrt{3}}{2} \]

\[ W = 500 \cdot \frac{\sqrt{3}}{2} \]

\[ W = 250\sqrt{3} \text{J} \]

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