Weight is an object’s force due to gravity.
Mass is the amount of matter something is made of. Mass is also how much inertia an object has: its resistance to acceleration.
Weight is a Force, so it can be calculated using Newton’s 2nd Law of Motion:
F = ma
or,
W = mg
The “F” in the equation is force of gravity, so it can be called Fg.
Fg (force of gravity) is the same thing as W (weight).
The “a” (acceleration) in this situation is acceleration due to gravity. This acceleration is commonly called “g.”
For our planet earth, gravitational acceleration has this value:
g = 9.8 m/s2
Sometimes we round that off to make head math easier:
g = 10 m/s2
Weight has units of force (Newtons) if you’re using metric.
(In U.S. units, you’d use pounds-mass and pounds-force)
Examples
Question 1: A house cat on planet earth has a mass of 5 kg. What’s the cat’s weight in Newtons?
Solution 1:
m = 5 kg
g = 10 m/s2
W = ???
W = mg
W = (5 kg)(10 m/s2)
W = 50 N
(The units work because 1 kg⋅m/s2 = 1 N)
Question 2: The same cat goes to Mars, where the gravitational acceleration is about 4 m/s2. What are a) the mass and b) the weight of this cat on Mars?
Solution 2:
a) The mass is still the same, because the cat is still made of the same amount of matter.
m = 5 kg
b) The cat’s weight is less now, because the force of gravity is smaller on the surface of Mars than it is on Earth.
m = 5 kg
g = 4 m/s2
W = mg
W = (5 kg)(4 m/s2)
W = 20 N