Spring Force Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Spring Force.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The restoring force exerted by a spring, proportional to how much it's stretched or compressed.

Stretch a spring twice as far, it pulls back with exactly twice as much force.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The negative sign means the restoring force always opposes the direction of displacement.

Common stuck point: Only valid within the elastic limit—stretch too far and the spring deforms permanently.

Sense of Study hint: When solving a spring force problem, first identify the spring constant k and the displacement x from the natural (unstretched) length. Then substitute into F = -kx. Remember the negative sign means the force always pulls back toward equilibrium — if you stretch right, the force acts left.

Worked Examples

Example 1

easy
A spring with spring constant k = 150 \text{ N/m} is stretched 0.2 \text{ m} from its natural length. What is the restoring force?

Solution

  1. 1
    Apply Hooke's law: F = -kx, where x is the displacement from equilibrium.
  2. 2
    |F| = kx = 150 \times 0.2 = 30 \text{ N}
  3. 3
    The negative sign indicates the force is directed opposite to the displacement (restoring force).

Answer

F = 30 \text{ N toward equilibrium}
Hooke's law states that the restoring force of a spring is proportional to its displacement from the natural length. The force always acts to return the spring to its equilibrium position.

Example 2

medium
A spring stretches 0.04 \text{ m} when a 2 \text{ kg} mass is hung from it. What is the spring constant? How much will it stretch with a 5 \text{ kg} mass? Use g = 9.8 \text{ m/s}^2.

Example 3

medium
A spring with k = 200 \text{ N/m} is compressed by 0.15 \text{ m}. Find the spring force and the elastic potential energy stored.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A spring (k = 300 \text{ N/m}) is compressed by 0.15 \text{ m}. What force does it exert, and how much elastic potential energy is stored?

Example 2

hard
Two springs are connected in series: k_1 = 200 \text{ N/m} and k_2 = 300 \text{ N/m}. A 12 \text{ N} force is applied. What is the total extension?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

force