Work Done by Gravity on a Freely Falling Body

When a body falls freely under gravity, the work done by gravity can be explained through the following details:

Definition of Work
Work is defined as the process of transferring energy from one object to another through the application of a force. In the case of gravity, work is done when a force is exerted on an object and causes it to move in the direction of the force.

Gravity and Free Fall
Gravity is the force that attracts two objects with mass towards each other. When an object falls freely under gravity, it means that the only force acting on the object is gravity. In this scenario, the object is in a state of free fall.

Work Done by Gravity
When a body falls freely under gravity, the work done by gravity can be calculated using the formula:

Work = Force × Displacement × cosθ

In the case of gravity, the force is the weight of the object, the displacement is the distance the object falls, and θ is the angle between the force and displacement vectors. Since the force of gravity acts vertically downwards and the displacement is also in the same direction, the angle between them is 0 degrees. Therefore, the value of cosθ is 1, and the formula simplifies to:

Work = Force × Displacement

In the context of a freely falling body, the force of gravity is equal to the weight of the object, which can be calculated using the formula:

Weight = mass × acceleration due to gravity

Conclusion
The work done by gravity on a freely falling body can be calculated using the formula: Work = Force × Displacement. In the case of gravity, the force is the weight of the object and the displacement is the distance the object falls. Since the force and displacement are in the same direction, the angle between them is 0 degrees and cosθ equals 1. Therefore, the formula simplifies to Work = Force × Displacement.

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