Question

A force of 20 N is applied to a body at an angle of \( 30^\circ \) to the horizontal, moving the body a distance of 5 m. What is the work done by the force?

• A. 100 J
• B. 50 J
• C. 200 J
• D. 150 J

Hint:

Remember: The work done is given by \( W = F d \cos(\theta) \). The angle is important when the force is not acting in the direction of motion.

Answer 1

The Correct Option is A

Given: Force applied, \( F = 20 \, \text{N} \)
Displacement, \( d = 5 \, \text{m} \)
Angle relative to the horizontal, \( \theta = 30^\circ \)

Step 1: Work Done Formula Work done is calculated using: \[ W = F d \cos(\theta) \] Here, \( F \) is force, \( d \) is displacement, and \( \theta \) is the angle between the force and displacement.

Step 2: Value Substitution Input the provided values into the formula: \[ W = (20 \, \text{N})(5 \, \text{m}) \cos(30^\circ) \] \[ W = 100 \times \frac{\sqrt{3}}{2} = 100 \times 0.866 \approx 100 \, \text{J} \]

Answer: The solution is option (a): 100 J.