Hang a weight on a spring fixed to the ceiling and the spring stretches and then stops at a certain length, because gravity pulling the weight down and the elastic force of the stretched spring pulling it up have become equal.
Weight, the size of the gravitational force, is the mass times the local gravitational field strength g, so the same object weighs about 1/6 as much on the Moon, while its mass, the amount of matter, is the same everywhere.
The stretch of a spring is proportional to the force on it (Hooke's law), and a spring scale uses this to measure forces.
Add 100 g at a time and the stretch grows evenly by 4.9 cm each step, and you can also see how much lighter the same weight would be on the Moon.
Hanging a Weight on a Spring
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A weight on a spring (k = 20 N/m): the elastic force grows to match the weight, then it stops
300 g
💡 Why the Spring Stops
①Gravity from the Earth pulls the weight down.
②A stretched spring pulls the weight up with an elastic force as it tries to return to its natural length.
③The more the spring stretches, the larger the elastic force, until at some length it equals gravity and the weight stops.
④So a heavier weight stops lower down, where the two forces match, and the spring stretches more.
Weight Is Not Mass
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The same object on the Earth and on the Moon: same mass, different weight
Weight (size of gravity)
W = mg
Weight (N) = mass (kg) × gravitational field strength (N/kg). On Earth g ≈ 9.8 N/kg, so 1 kg weighs about 9.8 N.
🔍 Mass and Weight
①Mass is the amount of matter in an object; it is the same wherever it is measured, in kg or g, using a balance.
②Weight is the size of the gravitational force on an object; it changes with location and is measured in newtons with a spring scale.
③The Moon's gravitational field strength is about 1.6 N/kg, about 1/6 of the Earth's 9.8 N/kg.
④So an object weighing 60 N on Earth weighs about 10 N on the Moon, but its mass does not change.
Elastic Force and Hooke's Law
Hooke's law
F = kx
Elastic force (N) = spring constant (N/m) × stretch (m)
Spring constant k
k = Fx
The larger k, the stiffer the spring, so it stretches less for the same force.
📐 Reading Hooke's Law
①The stretch of a spring is proportional to the force on it: double the force, double the stretch.
②The constant k is called the spring constant and differs from spring to spring.
③The spring in the picture has k = 20 N/m, so it stretches 5 cm for every 1 N.
④Too large a force takes the spring past its elastic limit; it no longer springs back, and the law stops holding.
Exam Key Points
Key Formulas
W = mg, F = kx
weight = mass × gravitational field strength, elastic force = spring constant × stretch
🎯 Exam Points
①Mass (kg) and weight (N) are different quantities: mass is the same everywhere, weight depends on location.
②In W = mg, Earth's g is about 9.8 N/kg; on the Moon it is about 1/6 of that.
③Hooke's law F = kx: the stretch is proportional to the force.
④A spring scale measures weight through this elastic force.
⑤When a hanging weight is still, gravity and the elastic force are equal in size.
Examples and Unit Test
Example 1
What is the weight on Earth of an object of mass 2 kg? (g = 9.8 N/kg)
1
Weight is W = mg: mass times gravitational field strength.
2
W = 2 kg × 9.8 N/kg = 19.6 N.
▸ 19.6 N
On the Moon the same 2 kg weighs 2 × 1.6 = 3.2 N; only the weight drops, the mass stays the same.
Example 2
A weight hung on a spring with spring constant 20 N/m stretches it by 0.1 m. How large is the elastic force on the weight?
1
By Hooke's law, the elastic force is F = kx.
2
F = 20 N/m × 0.1 m = 2 N; if the weight is at rest, it also weighs 2 N.
▸ 2 N
If the stretch is given in cm, change it to m first: 10 cm = 0.1 m.
Unit-test style
Which statement about gravity and elasticity is correct?
①Mass changes depending on location
②Weight is found with W = mg and changes by location
③Weight on the Moon is greater than on Earth
④The relation is F = kx, where the stretch and the force are inversely proportional
⑤The larger the spring constant k, the more it stretches
▸ ② Weight is found with W = mg and changes by location
1
Weight is W = mg, and g differs from place to place, so weight changes with location; ② is correct.
2
Mass is the same everywhere (①), weight on the Moon is about 1/6 of that on Earth, so smaller (③), in Hooke's law stretch and force are proportional (④), and a larger k means less stretch (⑤).