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. \( 433\, \text{J} \)
• C. \( 250 \, \text{J} \)
• 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

Calculate the Work Done by the Force

We are given the following data:

• Force applied \( F = 100 \, \text{N} \)
• Distance moved \( d = 5 \, \text{m} \)
• Angle between the force and the horizontal \( \theta = 30^\circ \)

Step 1: Recall the formula for work done

The formula for work done is: \[ W = F \cdot d \cdot \cos \theta \]

Step 2: Substitute the given values

\[ W = 100 \times 5 \times \cos 30^\circ \] \[ \cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866 \] \[ W = 100 \times 5 \times 0.866 = 433 \, \text{J} \]

Conclusion:

The work done by the force is \( 433 \, \text{J} \).

The correct answer is:

Option 2: 433 J