**What is gravity?**

According to Newton, **gravity** is the force of attraction between two objects having mass. This means that the two balls in the diagram have a gravitational force of attraction toward each other because they have mass.

The force of gravity between two objects depends on their mass and the distance between them.

If the blue ball has a mass of 2 kg and the green ball has a mass of 1 kg and they are 10 cm apart, what is the force of gravity between them?

**YIKES!! Look at the equation that Newton dreamed up. The G is a constant used no matter what or where the objects are.
**Newton publish work containing the Universal Gravitation Equation in July 1687. This gravity equation and many more of Newton’s ideas are still being used today.

You can find out more about Newton’s work as well as other scientists in

**“Scientist Through the Ages.**”

**Calculating the force of earth’s gravity on objects that are on or near earth’s surface. **

Using Newton’s universal gravitational formula, I calculated the force of gravity between the two balls in the diagram to be 13.4 x 10^{-9 }N, which is 0.00000000030 lbs. This force is too small to pull the balls toward each other because earth’s gravity on each ball keeps them in place. The pull of earth’s gravity on the blue ball is 19.6 N. Earth’s gravity on the green ball is 9.8N.

Newton’s Universal Gravity equation is needed to calculate the force of gravity between celestial bodies, such as the earth and the Sun. But, there is a much less complicated equation that can be used to calculate the force of gravity between things on earth. This equation was derived from Newton’s Universal Gravity equation. The diagram shows how this was done. Following is a breakdown of the equation that is used to calculate the force of gravity acting on everything on earth.

**F = m x g
**F= force of gravity between earth an an object, measured in newtons, N

m= mass of the object measured in kilograms, kg

g =

**earth’s**

**gravity constant**is 9.8 N/kg

The illustration shows children, a ball, and an elderly man standing on earth. The diagram is a model showing that no matter where an object is on earth, the object is pulled down. Down is a direction relative to where you are on earth. The direction of “down” is a line perpendicular to earth’s surface.

**1. **What is the force of earth’s gravity acting on the boy who has a mass of 30kg?

**Think:**

- The equation for calculating the force of earth’s gravity is
**F = m x g** - F is the force of earth’s gravity.
- m is the mass of the boy
- g is a constant, 9.8 N/kg
- F = 30 kg x 9.8 N/kg = 295 N

When typing, it is easy to write fraction like this: 9.8 N/m.

But, when units are part of an equation, they need to be considered. I strongly encourage you to teach kids to write fractions with a horizontal **fraction bar**.

Notice that the fraction bar separating the numerator 9.8 N from the denominator kg is horizontal.

Also note that I am suggesting that the fraction bar extend under the factor, 30 kg. I do this because it helps me to organize the information. When tutor math, I notice that kids often are not very neat when they write. Thus, I encourage them to extend the factor bar.

Notice that the kg unit in the numerator (above the fraction bar) cancels the kg unit in the denominator (below the fraction bar).

Note that the unit of newtons, N is left. This will be the unit in the answer.

Once the units have been considered, then consider the numbers and solve the problem.

The product of 30 x 9.8 is 295.

The answer is the 295 N.

Point out that measurement units must be considered and just like numbers, they cancel as in the above example. When units are part of the calculations, it is called **dimensional analysis.** Learning dimensional analysis in elementary and middle school makes chemistry and physics problems much easier to understand.

For most kids, using a horizontal fraction bar helps them better understand problems.

**Earth’s force of gravity is commonly referred to as the weight of objects.**

The force of gravity acting on the boy was calculated to be 295 N, thus the weight of the boy is 295 N.

In Texas, we generally measure our body weight in pounds, lb.

Following is another example of dimensional analysis, using a conversion factor relating pounds to newtons.

**Problem:**

The boy’s weight is 295 N, how many pounds it this equal to?

**Think:**

- The purpose is to determine how many pound 295 N is equivalent to.
- List facts that you know:

295 N is the weight that is to be changed to weight in pounds - The know relations betwee newtons and pounds is:

1 lb = 4.5N or 4.5N = 1 lb

Conversion factors are written as fractions: 1 lb/4.5N or 4.5 N/1 lb - You have all the information required to calculate the boys weight in pounds.
- Any time a conversion factor is needed, use what you know about dimensional analysis.

1. Write down the quantity that is to be changed.

2. Draw a fraction bar

3. Multiply by the conversion factor. Notice that the unit of the answer is in the numerator. Thus the conversion factor used is 1 lb/4.5 N.

4. Simplify the equation. The newton unit in the numerator cancels the newton unit in the denominator leaving only the pound unit for the answer.

5. Do the math, which is to divide 295 by 4.5.

**Gravity** is the force between two masses. This mean that while earth is pulling on you, at the same time you are pulling on the earth. It is like tug-of-war. While the force is the same, earth’s mass is so much greater than yours, so earth wins.