Gravitation always does negative work

Gravitation always does negative work. Question 48 options: True False

The correct answer and explanation is:

Answer: False

Explanation:

The statement “Gravitation always does negative work” is false because the work done by the gravitational force depends on the direction of the displacement relative to the force.

Work done by a force is defined as: W=F⃗⋅d⃗=Fdcos⁡θW = \vec{F} \cdot \vec{d} = F d \cos \theta

where:

• F⃗\vec{F} is the force vector,
• d⃗\vec{d} is the displacement vector,
• θ\theta is the angle between the force and displacement directions.

For gravitational force, which acts downward (towards the center of the Earth), the sign of work depends on the object’s movement:

1. Object moving downward (in the same direction as gravity):
   The force of gravity and displacement are in the same direction (θ=0∘\theta = 0^\circ). W=Fdcos⁡0∘=Fd>0W = Fd \cos 0^\circ = Fd > 0 This means gravity does positive work because it helps the object move, increasing its kinetic energy.
2. Object moving upward (against gravity):
   The displacement is opposite to the gravitational force direction (θ=180∘\theta = 180^\circ). W=Fdcos⁡180∘=−Fd<0W = Fd \cos 180^\circ = -Fd < 0 Here, gravity does negative work, opposing the object’s motion and reducing its kinetic energy.
3. Object moving perpendicular to gravity:
   If the displacement is perpendicular to the gravitational force (e.g., horizontal motion), θ=90∘,W=Fdcos⁡90∘=0\theta = 90^\circ, \quad W = Fd \cos 90^\circ = 0 In this case, gravity does no work on the object.

Summary:

• Gravitational force does not always do negative work.
• It does positive work when an object falls downward.
• It does negative work when an object moves upward against gravity.
• It does no work when the displacement is perpendicular to the gravitational force.

This is why the statement is false. The work done by gravity depends on the direction of the displacement relative to the gravitational force.