## 4.2 - Mass vs. Weight

Many people use the terms for mass and weight interchangeably. They are very different things. Mass is the amount of matter that an object is. It is the measure of the object’s inertia. MASS IS NOT A FORCE! Weight is the measure of the pull of gravity on a mass.

Mass is the same for an object in any direction. Weight is always in the down direction. The unit of weight is also the unit of force. Since weight is a force it is bound by Newton’s 2nd Law of Motion, F = ma. The mass in the equation is the mass of the object you have. The acceleration used is the acceleration due to gravity.

The acceleration due to gravity is so special and useful that it has its own symbol,

Mass is the more fundamental property because it never changes for an object as long as that object doesn’t lose some of its matter. Weight can change dramatically depending on your location and your motion.

If we modify Newton’s 2nd law equation slightly, we have a “shortcut” equation to calculate the weight of an object:

Mass is the same for an object in any direction. Weight is always in the down direction. The unit of weight is also the unit of force. Since weight is a force it is bound by Newton’s 2nd Law of Motion, F = ma. The mass in the equation is the mass of the object you have. The acceleration used is the acceleration due to gravity.

The acceleration due to gravity is so special and useful that it has its own symbol,

**g**. Another way to describe**g**is the**gravitational field strength**. On its surface, Earth’s gravitational field strength is 9.8 N/Kg, while on the surface of the moon it’s 1.67 N/Kg and Jupiter’s surface is 24.5 N/Kg. Although you would have the exact same mass on each of these planets, your weight would be VERY different.Mass is the more fundamental property because it never changes for an object as long as that object doesn’t lose some of its matter. Weight can change dramatically depending on your location and your motion.

If we modify Newton’s 2nd law equation slightly, we have a “shortcut” equation to calculate the weight of an object:

**W**stands for

**Weight**which is a force so the unit is the Newton;

**m**is for

**mass**in Kilograms; and

**g**is

**gravitational field strength**in Newtons/Kilogram. Not to get too technical but the units m/s/s and N/Kg mathematically describe the same thing.

**: Russian Kettlebells (a type of exercise device) come in many sizes. The one to the left is a mass of 20 Kg. No matter where this kettlebell travels in the universe (as long as parts don’t fall off it!), its mass will remain 20 Kg. However, the weight of this kettlebell depends on what is doing the pulling and the gravitational field strength. If it is on the Earth where the gravitational field strength is 9.8 N/Kg, then the weight of the kettlebell = 20 Kg x 9.8 N/Kg = 196 N. If this kettlebell was teleported to the moon (where the gravitational field strength is 1.67 N/Kg), its mass would remain 20 Kg but its weight would be 20 Kg x 1.67 N/Kg = 33.4 N.**

__Example__The twelve astronauts that walked on the moon had to wear environment suits to survive on the surface. These suits had to keep them warm or cool, provide air to breathe, take away the CO2 they exhaled, as well as other things. Each suit on Earth weighed over 300 pounds (~1400 N). Do you think that you could have walked around on the moon with a 300 pound suit on you? Neither could they. On the moon, the suits only weighed one sixth of that, 50 pounds (~230 N).

Though it doesn't actually happen, you can experience the sensation of weight change right here on Earth. When you are on a roller coaster it feels like your weight decreases as you go down the hills and it increases when you bottom out. When swimming, the water makes you feel relatively weightless. On an elevator, you feel heavier or lighter as you accelerate up or down.

Though it doesn't actually happen, you can experience the sensation of weight change right here on Earth. When you are on a roller coaster it feels like your weight decreases as you go down the hills and it increases when you bottom out. When swimming, the water makes you feel relatively weightless. On an elevator, you feel heavier or lighter as you accelerate up or down.

## Mass vs. Weight Video

**Free fall explained**

Earlier you investigated and learned that everything near the surface of the earth accelerates downward at the same rate, 9.8 m/s/s. We never really explained why that is though. Now Newton’s Laws help us explain it.

The gravitational force on an object is called its weight. An elephant weighs more than a mouse. An elephant also is made of more matter than a mouse. It has more inertia- a greater mass. Since we know that they both fall at the same rate of 9.8 m/s/s, the elephant should require a greater force pulling it because of its greater mass. And it does have a greater force pulling it- its weight!

An object that is ten times more massive than another has ten times more weight. The comparison of weight to mass is exactly the same.