Question:medium
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 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 \( 5 \, \text{m} \)?
Show Hint
Work done by a force is \( W = F d \cos \theta \). Always calculate the cosine of the angle between the force and displacement.
Updated On: Mar 28, 2026
- \( 500 \, \text{J} \)
\( 433\, \text{J} \)
\( 250 \, \text{J} \)
- \( 100 \, \text{J} \)
Show Solution
The Correct Option is B
Solution and Explanation
Determine the Work Performed by the Force
The provided data is:
- Applied Force \( F = 100 \, \text{N} \)
- Displacement \( d = 5 \, \text{m} \)
- Angle between force and displacement \( \theta = 30^\circ \)
Step 1: State the work done formula
The calculation for work done is: \[ W = F \cdot d \cdot \cos \theta \]
Step 2: Input the given values
\[ W = 100 \times 5 \times \cos 30^\circ \] \[ \cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866 \] \[ W = 100 \times 5 \times 0.866 = 433 \, \text{J} \]
Outcome:
The work done by the force is \( 433 \, \text{J} \).
The correct option is:
Option 2: 433 J
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