Physics / Unit 3: Forces and Newton's Laws
3.4 Weight, Mass and Normal Force
Notes
Mass is the amount of matter (kg) and is the same everywhere. Weight is the force of gravity: $W = mg$, in newtons.
- On Earth, $g = 9.8 \text{ m/s}^2$ (also $9.8 \text{ N/kg}$). On the Moon, $g \approx 1.6 \text{ m/s}^2$.
- On a flat surface with no vertical push or pull, the normal force equals the weight.
- In an elevator accelerating upward, $N = m(g + a)$; accelerating downward, $N = m(g - a)$. A scale reads the normal force.
- Example: a 70 kg student weighs $70 \times 9.8 = 686 \text{ N}$.
Practice
What is the weight of a 12 kg dog on Earth?
$W = mg = 12 \times 9.8 = 117.6 \text{ N}$.
An astronaut has a mass of 80 kg on Earth. What is her mass on the Moon?
Mass does not change with location; only weight does.
A 60 kg person stands on a scale in an elevator that accelerates upward at $2 \text{ m/s}^2$. What does the scale read?
$N = m(g + a) = 60(9.8 + 2) = 708 \text{ N}$.
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