Understanding the Work Done by Gravity in Free Fall

Understanding the Work Done by Gravity in Free Fall

Introduction

In the context of an object in free fall, the work done on the object by gravity can be calculated using the formula:

where: W is the work done on the object. F is the force acting on the object, which in this case is the weight of the object (F mg) where m is mass and g is the acceleration due to gravity. d is the distance fallen. θ is the angle between the force and the direction of motion. For an object in free fall, θ 0° and cos0° 1.

The simplified equation for work done by gravity on an object in free fall becomes:

Key Points

Work Done by Gravity

The work done by gravity on the object is positive because the force of gravity and the displacement of the object are in the same direction.

Potential Energy

As the object falls, gravitational potential energy is converted into kinetic energy. The work done by gravity is equal to the change in potential energy:

Kinematics

If an object falls from a height h, the work done by gravity when the object falls that height is:

This work results in an increase in the object's kinetic energy as it falls, according to the work-energy principle.
In summary, the work done by gravity on an object in free fall is equal to the weight of the object multiplied by the distance it falls, resulting in a change in the object's energy from potential to kinetic.
Free-Fall Scenarios
Perfect Free-Fall Scenario
In a perfect free-fall scenario, neglecting air resistance, the work done by gravity on the object is zero. Here’s the reasoning:
Free Preparation:
Open Google search for Work Definition: Work is defined as the force applied on an object multiplied by the distance the object moves in the direction of the applied force.
Free Fall and Displacement:
During free fall, the object moves in the same direction as the gravitational force downwards. This might seem like work is being done because the object is gaining speed.
Key Point:
However, in free fall there is no external force opposing the gravitational force. The object is already continuously falling due to gravity, and there is no additional force acting to cause that movement. Therefore, even though the object gains kinetic energy (energy of motion) as it falls, the work done by gravity itself is zero.
Heres another way to look at it: Imagine dropping a ball. Gravity pulls the ball downwards, but the ball doesn't push back against gravity. There is no opposing force, so no work is done in the technical sense.
Work Done by Other Forces:
It's important to consider situations where there might be work done:
Air resistance: In a real-world scenario, air resistance acts as an opposing force to gravity, slightly slowing down the falling object. In this case, air resistance would do negative work since it opposes the motion.
Catching the object: If you catch the falling ball, you exert an upward force to stop it. This external force would do positive work to overcome the object's momentum.
Understanding Energy Transfer
Even though the work done by gravity in a perfect free-fall scenario is zero, there is a transfer of energy happening:
Gravitational Potential Energy to Kinetic Energy: As the object falls, its gravitational potential energy due to its height decreases. This lost potential energy is converted into kinetic energy (energy of motion) as the object gains speed.
In conclusion, while the object's mechanical energy changes during free fall, with potential energy decreasing and kinetic energy increasing, the work done by gravity itself is zero in a perfect free-fall scenario without air resistance.