As mentioned in our previous blog, density is the relation of an object’s mass and volume, not its weight and volume. These two terms are often misunderstood and need clarification.

 

Understanding the Difference between Mass and Weight

Mass is defined as the amount of matter an object has. One of the qualities of mass is that it has inertia. For example, imagine a hockey puck resting on a frozen pond. It takes a certain amount of force to set the puck in motion. The greater the mass of the puck, the more force will be needed to move it. The same is true if the puck were sliding along the ice. It would continue to slide until a force is applied to stop the puck. The more massive the puck is, the more force will be needed to stop the motion of the puck. In other words, mass is a measure of how much inertia an object has. This is Newton’s first law of motion.

By contrast, the weight of an object depends on the “force” of attraction (gravity) between the object and the Earth (or another planet or object in space). Equation 1 is an expression of this force 

 

(1)             F = G • (M • m/r2)

 

where F is the force of attraction, M is the mass of the Earth, m is the mass of the object and r is the distance between the center of mass of the two objects. G is called the gravitational constant

 

From the Earth to the Moon

On Earth, a spring scale reads 100 g with an unknown mass attached at the bottom. To balance the scale on the right (Fig. 1), a 100-g mass is also needed.

If we were to take both scales to the moon, what would they read? (Hint: The moon’s gravity is 1/6th of that on Earth.) What would the spring scale read? How much mass would be needed to balance the 100-g mass on the balance beam on the right? Can you explain your answer?

On the moon, the spring scale would read 16.67 grams (100 g x 1/6). The balance scale on the right would still need 100 grams to balance it. 

 

What did the above exercise demonstrate?

It shows that the spring scale is measuring the force of gravity (that is, its weight) not mass since on Earth the spring was standardized to read 100 g (at sea level). The balance beam in Figure 1 measures mass by balancing the scale against a known mass. On the moon, the mass on the left side of the balance exerts less force, but less force is needed to balance it. So, 100 g is still required to be placed on the opposite side for the scale to be in balance whether the balance beam is on the Earth or the moon. Interestingly, the gram is the fundamental unit for mass, but it is often used to indicate weight in everyday earthbound situations.