Did you know that mass and weight are not the same? This lesson describes the difference between the two as well as the effect of gravity on weight. Examples are used to teach you how to calculate weight based on mass and acceleration of gravity.

## Newton’s Laws: Weight, Mass and Gravity

Most of us have seen images of men walking on the moon. Now, even though the astronauts are wearing really heavy suits, they seem to bounce around the surface of the moon with very little effort. How is it that we can bounce around on the moon with ease while jumping here on Earth requires a lot of effort? The answer to this question lies within the difference between mass and weight.**Mass** is a measure of how much matter an object contains, while **weight** is a measure of the force of gravity on the object. An object has the same composition, and therefore mass, regardless of its location.

For example, a person with a mass of 70 kg on Earth has a mass of 70 kg in space as well as on the moon. However, that same person’s weight is not the same since gravity is different in these locations. The person will weigh less on the moon because the moon has less gravity. To better understand the concepts of weight and mass, we must first consider gravity and its effect on objects.

## What is Gravity?

So what is gravity? **Gravity** is the attractive pull between two objects that have mass. The strength of gravity is directly proportional to the amount of mass of each object.

In other words, the larger the objects, the greater the gravitational attraction between them. For example, the gravitational pull you experience on Earth is much greater than it would be on the moon because the Earth’s mass is greater. An object with twice as much mass will exert twice as much gravitational pull on other objects.

On the other hand, the strength of gravity is inversely related to the square of the distance between two objects. For example, if the distance between two objects doubles, meaning they’re twice as far apart, the gravitational pull decreases by a factor of 4.

This is because 2 squared is equal to 4. This means the effect of distance on gravitational attraction is greater than the effect of the masses of the objects.

## Gravity as a Force

Gravity is a force. A **force** is simply a push or a pull experienced by objects that interact with each other. The interaction can be direct or at a distance, which is the case of gravity.

**Newton’s laws** tell us that if an unbalanced force acts on an object, it will change the object’s state of motion. In other words, the object will accelerate. Since gravity is a force, gravity causes objects to accelerate.

## Acceleration Due to Gravity

Let’s look at an example of how gravity causes acceleration. If you drop a ball from a cliff, you will notice that the speed increases as it falls – it accelerates due to gravity. We have determined the **acceleration of gravity** is 9.8 m/sec^2 – that is, for free-falling objects on Earth.

**Free falling** simply means no other forces, except gravity, are acting on the object. For example, any effect of wind resistance would be neglected. The velocity of a free-falling object increases by 9.8 meters per second every second.Let’s look at the speed of the ball as it drops over time.

This is going to help us understand how gravity causes acceleration.

As you see on the screen, the ball will accelerate to a speed of 9.8 meters per second in the first second of travel. Over the next second, the speed of the ball will again increase by 9.

8 meters per second, meaning it’s traveling at 19.6 meters per second. The same thing will happen during the third second of time, so the ball will be traveling at 29.4 meters per second. With each second, the ball’s speed increases by 9.8 meters per second.The acceleration of gravity is so important that it has its own symbol.

It is often abbreviated with the letter *g*. ** g = 9.8 m/sec^2** – that’s the acceleration of gravity here on Earth for free-falling objects.

## Gravity and Weight

Well, what about weight? Weight is a measure of the force of gravity acting on an object. According to Newton’s laws of motion, force is directly proportional to both mass and acceleration, and the equation for force is ** F = m * a**, where

*m*= mass and

*a*= acceleration. We can use this equation to solve for weight.

All objects on Earth, whether they are falling, thrown, or even sitting still, experience the effect of gravity. Therefore, we can determine the weight of an object using the acceleration of gravity.

## Calculation of Weight

Let’s look at an example. How much does a 100-kg man weigh on Earth?Let’s first recall the formula for force.

*F* = *m* * *a*Now substitute weight for force and the acceleration of gravity (*g*) for acceleration.Weight = *m* * *g*Now plug in the values for *m* and *g* and solve for weight.Weight = 100 kg * 9.8 m/sec^2Weight = 980 kg * m/sec^2A newton (N) of force equals 1 kg * m/sec^2; therefore, we can say the man has a weight of 980 newtons.

**Weight = Force = 980 N**. Now, there are approximately 4.5 newtons in a pound. Therefore, the person in our example weighs about 218 pounds.

## Big Misconception

Let’s look at a common misconception. If a 100-kg man and a 10,000-kg elephant jumped off a cliff, which would hit the ground first? One might think the elephant would land first due to its greater mass. However, they both land at the same time (assuming they’re both free falling). We can use some simple math to understand this phenomenon by rearranging the formula for force to solve for acceleration.First, recall the formula for force.*F* = *m* * *a*Now, let’s rearrange and solve for acceleration.*a* = *F*/*m*As seen by the formula, acceleration is directly proportional to the force and inversely proportional to the mass of the object.

Increased force tends to increase acceleration, while increased mass tends to decrease acceleration. Now, the elephant in our example has 100 times as much mass as the person – this would decrease its acceleration.However, because the elephant has 100 times the mass, it experiences 100 times as much gravitational force. The greater force exerted on more massive objects is offset by the inverse influence of greater mass. Therefore, all objects free fall at the same acceleration regardless of their mass.

## Lesson Summary

In summary, **mass** is a measure of how much matter an object contains, and **weight** is a measure of the force of gravity acting on the object. **Gravity** is the attraction between two objects that have mass.

The amount of gravity is directly proportional to the amount of mass of the objects and inversely proportional to the square of the distance between the objects.Gravity is a force that increases the velocity of falling objects – they accelerate. The **acceleration of gravity** is abbreviated by the letter *g*, and it has a value of 9.8 m/sec^2. All objects on Earth, regardless of their mass, accelerate due to gravity at the same rate – that is, 9.8 m/sec^2. The weight of an object can be calculated using the formula for force – ** F = m * a** – where

*F*equals the weight of the object and now the acceleration (

*a*) is the acceleration of gravity (

*g*).

## Learning Outcomes

By the end of this lesson, you should be able to:

- State the difference between mass and weight
- Recall the value for the acceleration of gravity
- Use the formula for force to calculate the weight of an object
- Explain why all free falling objects released together will hit the ground simultaneously