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# Energy due to Gravity of Falling Objects

by Ron Kurtus (24 May 2013)

An object held at a given height above the ground has an initial potential energy. When it is dropped, it gains kinetic energy. The total energy of the object is then used to find the velocity when the object hits the ground.

You can calculate the **PE**, **KE** and total energy (**TE**) for an object that is dropped. You can then verify that the final velocity is the same as obtained from the gravity derivations.

Questions you may have include:

- What is the potential energy for a dropped object?
- What is its kinetic energy?
- What is the total energy and final velocity for a falling object?

This lesson will answer those questions. Useful tool: Units Conversion

## Potential energy for falling object

The equation for the object's initial **PE** with respect to gravity is::

PE_{i}= mgh

where

**PE**is the initial potential energy in joules (J) or foot-pounds (ft-lbs)_{i}**m**is the mass of the object in kg-mass or pound-mass**g**is the acceleration due to gravity (9.8 m/s^{2}or 32 ft/s^{2})**h**is the height above the ground in m or ft

Note: Potential energy is also sometimes abbreviated asU.

When the object reaches the ground, **h =** 0 and thus the final potential energy is:

PE0_{f}=

Note: In reality, there is still a gravitational force on the object at the surface of the Earth, so the object has a gravitational potential energy at that point. But since the object cannot go anywhere, we say itsPEfrom gravity is zero.

## Kinetic energy for falling object

Kinetic energy (**KE**) is the energy of motion. Since the object is not moving at the initial position, the initial **KE** is:

KE0_{i}=

Once the object is released, it accelerates downward. When the object reaches the ground, its kinetic energy is:

KE_{f}= mv_{f}^{2}/2

where

**KE**is the kinetic energy at the ground in joules (J) or foot-pounds (ft-lbs)_{f}**v**is the downward velocity of the object at the ground in m/s or ft/s_{f}

## Total energy for falling object

The total energy of the object is:

TE = PE + KE

The total energy is a constant value, provided no external forces besides gravity act on the object. Thus, the initial total energy equals the final total energy:

TE_{i}= TE_{f}

PE_{i}+ KE_{i}= PE_{f}+ KE_{f}

When the object is simply dropped,

mgh +0 = 0+ mv_{f}^{2}/2

mgh = mv_{f}^{2}/2

### Final velocity for falling object

From that equivalence, you can determine the final velocity of the dropped object. Divide by **m** and multiply by 2:

v=_{f}^{2}2gh

v_{f}= √(2gh)

This is equivalent to **v = √(2gy)** that is given in Velocity Equations for Falling Objects.

## Summary

Potential energy with respect to gravity is **PE = mgh**. When the object is dropped, thrown downward or projected upward, its kinetic energy becomes **KE = mv ^{2}/2**, along with a factor of the initial velocity.

The sum of the **PE** and **KE** is the total energy, which is a constant. Equating the initial total energy with the final total energy, you can determine the final velocity of the object.

You can succeed

## Resources and references

### Websites

**Gravity and Potential Energy** - University of Alaska

### Books

**Top-rated books on Simple Gravity Science**

**Top-rated books on Advanced Gravity Physics**

## Questions and comments

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## Where are you now?

Gravity and Gravitation topics## Energy due to Gravity of Falling Objects