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# Equivalence Principle of Gravity

by Ron Kurtus (revised 18 February 2010)

Intuitively, you would think that a heavier object would fall to the ground faster than a lighter object. However, that is not the case. The *Equivalence Principle of Gravity* (also called the *Weak Equivalence Principle* or *Uniqueness of Free Fall Principle*) states that all objects fall at the same rate, assuming negligible air resistance.

By examining the equation for the force of gravity, you can see that the value of the acceleration due to gravity is a constant and is independent of the mass of the object. A constant acceleration means that objects fall at the same rate. This principle has been proven experimentally many times.

Questions you may have include:

- How is acceleration due to gravity constant?
- What happens when you drop two balls at the same time
- How has this principle been proven?

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

## Acceleration due to gravity is constant

You can see that the acceleration due to gravity is constant by examining the force of gravity on objects relatively close to Earth:

F = mg

where

**F**is the force newtons (N) or pound-force (lb)**m**is the mass of the object in kilograms (kg) or pound-mass**g**is the acceleration due to gravity: 9.8 m/s^{2}or 32 ft/s^{2}

What this means is that the force from the Earth's gravity is proportional to the mass of the object. Objects with greater mass feel a greater the force on them.

However, the acceleration due to gravity, **g**, is the same for all objects, no matter what their mass. This means that all objects will accelerate or fall at the same rate, provided they are not affected by air resistance.

## Balls fall at same rate

Dropping two objects of different mass from exactly the same height and exactly the same time will result in them falling at the same rate and hitting the ground simultaneously.

Balls of different mass fall at the same rate

If one or both objects are noticeably affected by air resistance, another factor comes into play, and the rule does not hold. For example, dropping a golf ball and a feather will result in the golf ball hitting the ground before the feather, which is greatly affected by air resistance and air currents.

Notethat any object you drop is somewhat affected by air resistance. However, some are barely affected, such that the rule still holds.

## Experimental verification

The fact that the acceleration due to gravity is independent of the mass of the objects has been verified many times.

In the 1600s, Galileo Galilei was said to have dropped two balls of different mass from the Leaning Tower of Pisa to prove that objects of different mass fall at the same rate. Some historians doubt whether he actually did the experiment at Pisa, but the experimental results are documented.

You can verify this experiment yourself by standing on a chair and dropping two balls or objects of different weights at exactly the same time. This is a rough experiment, but it can demonstrate the principle.

## Summary

The *Equivalence Principle of Gravity* states that all objects fall at the same rate, assuming negligible air resistance. The force of gravity equation shows that the value of the acceleration due to gravity is a constant and is independent of the mass of the object.

A constant acceleration means that objects fall at the same rate. This principle has been proven experimentally many times. The most famous verification was when Galileo apparently dropped two balls of different mass from the Leaning Tower of Pisa.

Weigh the question before making a decision

## Resources and references

### Websites

**Test of Weak Equivalence Principle** - Precision Astronomy Group of Harvard-Smithsonian Center for Astrophysics

**Feather & Hammer Drop on Moon** - YouTube video

### Books

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

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

## Questions and comments

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## Equivalence Principle of Gravity