Mass, Weight & Normal Force
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Mass (kg) is how much stuff an object has. Weight is the gravitational force on it, Fg = mg, in newtons. The normal force is a surface pushing straight out on whatever touches it, and it is only as big as it needs to be. It equals mg only when nothing else pushes up or down and there’s no vertical acceleration.
1. Mass vs. weight
A 60 kg student weighs (60 kg)(10 N/kg) = 600 N on Earth.
On the Moon, g is about 1.6 N/kg, so she weighs about 100 N. Her mass is still 60 kg: she has just as much stuff.
2. The normal force adjusts
A scale reads the normal force, not your weight. Normally they match, but not always.
In an elevator, take up as positive: Fn − mg = ma. Accelerating up makes Fn bigger than mg; accelerating down makes it smaller.
Pushing down on a box makes the floor push back harder. Pulling up on it with a rope makes the floor push less.
3. Example, then try it
A 60 kg student stands on a scale in an elevator that is accelerating downward at 2 m/s². What does the scale read?
Up = +, so a = −2 m/s²: Fn − mg = ma
Fn = m(g + a) = 60(10 − 2) = 480 N, less than her 600 N weight.
A 5.0 kg box sits on a table. (a) You push down on it with 20 N. What is the normal force? (b) Instead, you pull up on it with a 20 N rope. Now what is the normal force?
Weight: mg = (5.0)(10) = 50 N down.
(a) The table must hold up the weight and your push: Fn = 50 + 20 = 70 N.
(b) The rope helps hold the box up, so the table pushes less: Fn = 50 − 20 = 30 N.
Check: if the rope pulled up with more than 50 N, the normal force would hit zero and the box would lift off.
Answer: (a) 70 N, (b) 30 N. Same box, same weight, three different normal forces.
4. Common mistakes
An astronaut with a mass of 70 kg travels to the Moon. What happens to her mass and her weight?
Mass is the amount of stuff, so it stays 70 kg. Weight is mg, and g on the Moon is smaller, so her weight decreases.
Ready to practice?
5 questions on Mass, Weight & Normal Force, each with a hint and an explanation for every wrong answer.