Question

A force of \( 100 \, \text{N} \) is applied to an object at an angle of \( 30^\circ \) to the horizontal. What is the work done by the force in moving the object a distance of \( 5 \, \text{m} \)?

• A. \( 500 \, \text{J} \)
• B. \( 250 \, \text{J} \)
• C. \( 433 \, \text{J} \)
• D. \( 100 \, \text{J} \)

Hint:

Work done by a force is \( W = F d \cos \theta \). Always calculate the cosine of the angle between the force and displacement.

Answer 1

The Correct Option is B

Step 1: Use the formula for work done \[ W = F d \cos \theta \] Where: - \( W \) is the work done - \( F \) is the applied force - \( d \) is the distance moved - \( \theta \) is the angle between the force and the direction of motion Given: - \( F = 100 \, \text{N} \) - \( d = 5 \, \text{m} \) - \( \theta = 30^\circ \) Substitute the values into the formula: \[ W = 100 \times 5 \times \cos(30^\circ) = 100 \times 5 \times 0.866 = 250 \, \text{J} \] Answer: Therefore, the work done is \( 250 \, \text{J} \). So, the correct answer is option (2).