Question

A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.

Answer 1

Work Done by Gravitational Force on a Mass Moving Horizontally 

1. Given

• Mass of the object: \( m = 10\,\text{kg} \)
• Displacement: Horizontal from point A to point B
• Gravitational acceleration: \( g = 9.8\,\text{m/s}^2 \)

2. Formula for Work Done

Work done by a force is given by:

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

• \( F \) = magnitude of the force
• \( d \) = displacement of the object
• \( \theta \) = angle between the force and displacement

3. Work Done by Gravitational Force

Gravitational force acts vertically downward: 
\( F_g = m g = 10 \times 9.8 = 98\,\text{N} \)

Displacement is horizontal. Angle between gravity (vertical) and displacement (horizontal) is: 
\( \theta = 90^\circ \)

Substituting in the formula: 
\( W = F \cdot d \cdot \cos\theta = 98 \cdot d \cdot \cos 90^\circ \) 
\( \cos 90^\circ = 0 \) 
\( W = 0 \)

4. Explanation

Since the displacement is perpendicular to the direction of gravitational force, gravity does no work on the object. Only forces along the direction of motion can do work.

5. Conclusion

Work done by the gravitational force = 0 J