Explanation of the Overview of the Force of Gravity by Ron Kurtus - Succeed in Understanding Physics. Key words: physical science, Isaac Newton, Universal Gravitation, acceleration, mass, weight, Earth, Moon, planets, Sun, School for Champions. Copyright © Restrictions

# Overview of the Force of Gravity

by Ron Kurtus (revised 13 September 2013)

Gravity is a force that attracts objects toward the Earth. It is an approximation of the gravitational force that attracts objects of mass toward each other at great distances. Gravity applies to objects on or near the surface of the Earth.

The equation for the force of gravity is F = mg, where g is the acceleration due to gravity. Units can be designated in metric (SI) or English system. The equation also indicates the weight of an object.

The major feature of this force is that all objects fall at the same rate, regardless of their mass. Gravity on the Moon and on other planets have different values of the acceleration due to gravity. However, the effects of the force are similar.

Questions you may have include:

• What is the gravity equation?
• What is the most outstanding characteristic of gravity?
• What is gravity elsewhere?

This lesson will answer those questions.

Useful tool: Metric-English Conversion

## Gravity equation

According to Newton's Law of Universal Gravitation, gravitation is the force that attracts objects toward each other. For objects relatively close to the Earth, this force is called gravity, and its equation is:

F = mg

where

• F is the force pulling objects toward the Earth
• m is the mass of the object
• g is the acceleration due to gravity; this number is a constant for all masses of matter
• mg is the product of m times g

Note: For verification that the gravitational force equals the force of gravity for objects close to Earth, see Gravity Constant Factors.

### Acceleration due to gravity

The acceleration due to the force of gravity on Earth is designated by g. Its value is:

g = 9.807 meters per second-squared (m/s2) in the metric or SI system of measurement

g = 32.2 feet per second-squared (ft/s2) in the English system of measurement

Note: Since most textbooks use g = 9.8 m/s2 and 32 ft/s2, we will also use the rounded-off version in these lessons.

In the equation F = mg, you must use the same measurement system for mass, m, as you do for g.

Note: Some textbooks carelessly define g as the acceleration of gravity. That is incorrect and misleading, since gravity does not accelerate. The expression should be the acceleration due to gravity, which is correct description of g.

Care must be taken in defining scientific terms.

### Weight and mass

The weight of an object of a given mass is the force of gravity on that object:

w = mg

where

• w is the weight in newtons (N) or pound-force (lb)
• m is the mass in kilograms or pound-mass (lb-mass)

Note: There is often confusion concerning the designation of weight and mass.

Although a kilogram is supposed to be a unit of mass, it is often used to designate weight. You must be aware that weight of 1 kg of mass is w = 9.8 newtons.

Also, a pound is supposed to be a force, but is often called a mass. The mass of 1 pound-force is 1/32 pound-mass.

Again, you must be precise in stating scientific terms.

### Weighing an object

You can find the weight of an object on a calibrated scale—usually with a spring resisting the force of the weight.

The mass of an object can be measured with a balance scale, comparing with an object of a given mass.

## Objects fall at the same rate

The most outstanding characteristic of gravity is the fact that all objects fall at the same rate—assuming the effect of air resistance is negligible. This is because the acceleration due to gravity, g, is a constant for all objects, no matter what their mass.

This seems counterintuitive, since you would expect a heavy object to fall faster than an object that weighed less. But it is a fact. Try dropping two objects at the same time, from the same height, making sure they are heavy enough not to be affected by air resistance. You will see they hit the ground at the same time.

## Gravity elsewhere

When you talk about gravity, you mean gravitation near the Earth. However, the same gravity equation holds for objects near the Moon or other planets, except that the value of g is different. In those cases, you typically tell where the gravity is, such as "gravity on the Moon" or "gravity on Mars."

### Gravity on the Moon

The force of gravity on the Moon is approximately 1/6 of that on the Earth for a given mass. Thus:

Fm = mgm

where

• Fm is the force or weight on the Moon
• m is the mass of an object
• gm is the acceleration due to gravity on the Moon

The value for gm is 1.6 m/s2 or 5.3 ft/s2.

### Weight and mass on the Moon

The value for gm is approximately 1/6 of the value for g on Earth. Thus, an object on the Moon would weigh about 1/6 of its weight on Earth.

Using a spring scale, if you weigh 60 kg (132 pounds) on the Earth, you would weight only 10 kg (22 lbs) on the Moon. However, using a balance scale on both Earth and the Moon, your mass would be the same.

### Dropped objects

If you dropped two objects of different weights on the Moon, they would fall to the ground at the same rate. You wouldn't have to worry about the effect of air resistance, since there is no air on the Moon.

Since gm = g/6, the objects would fall at a slower rate.

(See Gravity Equations for Falling Objects and then apply gm to get the different values.)

## Summary

Gravity is the force that pulls objects toward the Earth. It is a special case of gravitation. The equation for the force due to gravity is F = mg, resulting in the fact that all objects fall at the same rate, regardless of their mass. Gravity on the Moon and gravity on other planets have different values of the acceleration due to gravity, but the effects of the force are similar.

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## Resources and references

Ron Kurtus' Credentials

### Websites

Gravity Resources

Force of Gravity - Universe Today Magazine

Earth's gravity - Wikipedia

How does gravity work? - How Stuff Works

Standard gravity - Average value, as compared to variation due to position on Earth - Wikipedia

International Gravity Formula - Variation of gravity with distance from equator - Geophysics dept. University of Oklahoma

I feel 'lighter' when up a mountain but am I? - National Physics Laboratory FAQ

### Books

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