# Why the work done by us and gravitational force is equal when we lift an object?

The work done by us and gravitational force is equal when we lift an object, is due to the law of conservation of energy.

Law of conservation of energy - It states that energy can neither be created nor be destroyed. However, it may be transformed from one form to another. If we take all forms of energy into account, the total energy of an isolated system always remains constant, it is said to be conserved over time. All the forms of energy follow the law of conservation of energy.

So, here when we lift an object, then we'd have to give a force greater than that of gravity to break its inertia and set it into motion.

If an object is lifted, work is done against the force of gravity, and when work is done energy is transferred to the object and it gains gravitational potential energy or GPE.
Now, if the object falls from a certain height, the same amount of work would have to be done by the force of gravity to bring it back to the Earth’s surface.

The amount of gravitational potential energy an object has on Earth depends on its: mass, and height above the ground.

So, the gravitational potential energy of an object raised above the Earth’s surface can be calculated using the equation:
Gravitational potential energy = mass x gravitational field strength x vertical height raised

For example - If an object at a certain height has 4000 J of gravitational potential energy, we can say that:
4000 J of work has been done in getting the object to that height from the ground, and 4000 J of work would have to be done to bring it back to the ground.

Thus, due to the Principle of Conservation of Energy, we can say that:
Gravitational potential energy = work done

To understand better, understand the Gravitational force and Gravitational potential energy (GPE).
Gravitational force - It is an attractive force that appears between any two masses. Force affects an object/a mass.
The formula for gravitational force is given as:
$F=mg$

Gravitational potential energy (GPE) - It is the amount of energy possessed by a mass due to its positions in the gravitational field. Energy is something that mass possesses.
${E}_{gp}=mgh$

The apple (mass) that falls from the tree is affected by the gravitational force and the apple possesses gravitational potential energy or simply gravitational energy.

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Updated on: 10-Oct-2022

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