Weight vs Mass
How is weight different to mass?
The mass of an object is the amount of stuff that's in it. It is a scalar measurement (i.e. it only has magnitude), and we can measure it by using scales. It doesn't change irrespective of where an object is situated.
Why does weight change?
The gravitational constant doesn't change, but weight does. Why is this? The best way to understand this is to work through an example. Let's take this dumbbell, and work out how its weight would vary if you were to take it from the surface of the earth to the surface of the moon.
Its weight on earth would be calculated using this formula:
Its weight on the moon would be calculated using this formula:
Its weight changes because the mass and radius of the earth and moon are different compared to each other; but how different?
Weight changes between the earth and the moon
Roll over the image below to see how the earth's mass and radius compares to that of the moon.
Based on what we learned here about how changes in mass and radius influence the pull of gravity:
- the smaller mass of the moon will reduce the dumbbell's weight by 81 times cf. to its weight on the earth.
- the smaller radius of the moon will increase the dumbbell's weight by 13 times cf. to its weight on the earth (this is calculated by squaring 3.6).
What's the overall effect of the move? To find out we just need to divide 81 by 13. The result is that the weight of the dumbbell on the moon will be 81/13 = approximately 6 times smaller than its weight on earth. Want to double check this? Check this out: