Gravity & Elasticity

Hang a mass on a spring and gravity pulls down while the elastic force pulls up until they balance. Weight is W=mg and depends on location; mass is the same everywhere. By Hooke's law F=kx the stretch is proportional to force, and a larger k means a stiffer spring. Slide the mass to watch the stretch and compare weight on Earth and the Moon.

Hanging a Mass on a Spring?

Mass3 kg

💡 Why Does the Spring Stretch?

①Gravity pulls the mass downward

②The spring stretches and exerts an upward elastic force

③When forces balance, motion stops (equilibrium)

④Larger mass → more stretch

Gravity — Weight vs Mass

Weight (gravity)

W = mg

Weight (N) = mass (kg) × gravitational acceleration (m/s²)

🔍 Mass vs Weight

①Mass (kg): amount of matter → constant everywhere

②Weight (N): magnitude of gravity → varies by location

③g ≈ 9.8 m/s² on Earth, ≈ 1.6 m/s² on the Moon

④Lunar weight ≈ 1/6 of Earth's

Elastic Force and Hooke's Law

Hooke's Law

F = kx

Elastic force (N) = spring constant (N/m) × extension (m)

Spring Constant k

k = Fx

Larger k means a stiffer spring (harder to stretch)

📐 Hooke's Law Essentials

①Spring extension is proportional to force

②Proportionality constant k = spring constant

③Higher k → less stretch for the same force

④Beyond elastic limit, the law no longer holds

Exam Key Points

Core Summary

W = mg, F = kx

Gravity = mass × g; elastic force = k × extension

🎯 Exam Key Points

①Weight ≠ mass (units: N vs kg)

②W = mg with g ≈ 9.8 on Earth

③Hooke's law: F = kx (proportional)

④Spring scale measures weight via elastic force

⑤Equilibrium: gravity = elastic force (rest)

Examples and Unit Test

Example 1

What is the weight on Earth of an object with a mass of 2 kg? (g = 9.8 m/s²)

Weight is found with W = mg (mass times gravitational acceleration).

W = 2 kg × 9.8 m/s² = 19.6 N.

▸ 19.6 N

Weight W = mg, so the same mass weighs differently where g is different.

Example 2

A weight hung on a spring with a spring constant of 20 N/m stretches it 0.1 m. What is the size of the elastic force?

By the law of elasticity, the elastic force F = kx (spring constant times the stretch).

F = 20 N/m × 0.1 m = 2 N.

▸ 2 N

By the relation F = kx, the stretch of a spring is proportional to the force.

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

Weight is W = mg, and since g differs by location, weight also changes by location.

Mass is constant everywhere (①), weight on the Moon is about 1/6 of that on Earth (③), in the relation F = kx the stretch and force are proportional (④), and a larger k stretches less (⑤).

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Types of Forces

Density

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