Spring Force Examples: 47 Problems with Answers

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: Spring Force asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to spring force but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

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?

Answer

F = 30 N toward equilibrium

First step

Apply Hooke's law:

F = -kx

, where

x

is the displacement from equilibrium.

Full solution

2
$∣ F ∣ = k x = 150 \times 0.2 = 30 N$
3
The negative sign indicates the force is directed opposite to the displacement (restoring force).

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

Hanging mass in equilibrium: spring force balances weight

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.

Example 4

medium

0.5 \text{ kg}

mass hangs at rest from a vertical spring, stretching it

0.1 \text{ m}

. Find the spring constant. Use

g = 9.8 \text{ m/s}^2

Equilibrium: F_s = W = 4.9 N; then k = F/x = 4.9/0.1 = 49 N/m

Example 5

medium

A spring exerts

12 \text{ N}

when stretched

0.06 \text{ m}

. How much will it stretch under a

20 \text{ N}

force?

Example 6

hard

Two identical springs each of stiffness

k

are connected in parallel and support a mass

m

. What is the effective spring constant of the combination?

Example 7

medium

A spring is compressed

0.2 \text{ m}

and used to launch a

0.5 \text{ kg}

block on a frictionless surface. If

k = 200 \text{ N/m}

, find the block's speed after release.

Energy conservation: ½kx² = ½mv²; v = 4 m/s

Example 8

hard

0.4 \text{ kg}

mass on a horizontal spring oscillates with

k = 100 \text{ N/m}

. Find the period of oscillation.

Example 9

medium

A horizontal spring is stretched

0.20 \text{ m}

from equilibrium and released. The mass is

0.25 \text{ kg}

and

k = 100 \text{ N/m}

. Find its maximum speed.

Example 10

medium

A spring is stretched from

0.05 \text{ m}

0.15 \text{ m}

beyond its natural length. With

k = 200 \text{ N/m}

, find the work done by the external pull.

Example 11

challenge

2 \text{ kg}

block on a frictionless incline of

30°

is held against a spring (

k = 500 \text{ N/m}

) compressed by

0.20 \text{ m}

. When released, how far up the incline (measured from the spring's natural length position) does the block slide? Use

g = 9.8 \text{ m/s}^2

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?

Restoring force F = kx = 300×0.15 = 45 N; PE = ½kx²

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?

Example 3

easy

A spring with

k = 200

N/m is stretched

0.1

m. Find the magnitude of the spring force.

Example 4

easy

A spring stretches

0.05

m under a

10

N force. Find its spring constant.

Example 5

easy

A spring (

k = 500

N/m) is compressed

0.04

m. Find the spring force magnitude.

Example 6

easy

A spring force of

30

N corresponds to a stretch of

0.15

m. Find the spring constant.

Example 7

easy

In Hooke's law

F = -kx

, what does the negative sign indicate?

Example 8

easy

A spring stretches

0.2

m when a

4

N weight hangs from it. Find the spring constant.

Spring force equals weight at equilibrium; use kx = F to find k

Example 9

easy

A spring (

k = 100

N/m) exerts

25

N. How far is it stretched?

Example 10

easy

Spring A doubles its stretch. By what factor does its spring force change?

Example 11

medium

2

kg mass hangs from a spring (

k = 400

N/m,

g=10

m/s

^2

). Find the equilibrium stretch.

At equilibrium: kx = mg, so x = mg/k

Example 12

medium

Two springs (

k_1 = 100

N/m,

k_2 = 300

N/m) in parallel support a load. Find the effective spring constant.

Example 13

medium

Two springs (

k_1 = 200

N/m,

k_2 = 200

N/m) in series support a load. Find the effective spring constant.

Example 14

medium

A spring (

k = 50

N/m) is stretched

0.2

m. Find the elastic potential energy stored.

Example 15

medium

0.5

kg block on a frictionless surface is attached to a spring (

k = 200

N/m) stretched

0.1

m and released. Find its initial acceleration.

Spring force is net force; initial acceleration = F/m

Example 16

medium

A spring stretches

0.1

m under a

5

N force. How much force is needed to stretch it

0.3

Example 17

medium

A vertical spring (

k = 100

N/m) compresses

0.2

m under a block placed on it (

g=10

m/s

^2

). Find the block's mass.

Example 18

medium

A spring is stretched from

0.1

m to

0.3

m. Find the extra elastic energy stored (

k = 100

N/m).

Example 19

medium

A spring (

k = 300

N/m) is stretched

0.2

m. Find the spring force magnitude.

Example 20

challenge

0.5

kg block on a frictionless surface compresses a spring (

k = 800

N/m) by

0.1

m and is released. Find the block's launch speed.

Example 21

challenge

1

kg mass on a spring (

k = 100

N/m) oscillates. Find its period.

Example 22

challenge

2

kg block on a

30^\circ

frictionless incline is held by a spring along the slope (

g=10

m/s

^2

). The spring (

k = 250

N/m) stretches to hold it. Find the stretch.

Example 23

easy

A spring with

k = 250 \text{ N/m}

is stretched

0.08 \text{ m}

. Find the magnitude of the restoring force.

Example 24

easy

3 \text{ N}

pull stretches a spring by

0.06 \text{ m}

. Find the spring constant.

Example 25

medium

A spring with

k = 400 \text{ N/m}

is compressed by

0.05 \text{ m}

. Find the elastic potential energy stored.

Example 26

easy

A spring with

k = 80 \text{ N/m}

is stretched

0.25 \text{ m}

. Find the magnitude of the spring force.

Example 27

medium

A vertical spring stretches

0.04 \text{ m}

when a

0.2 \text{ kg}

mass is hung from it. How much will it stretch with a

0.5 \text{ kg}

mass?

Example 28

hard

Two springs with

k_1 = 100 \text{ N/m}

and

k_2 = 100 \text{ N/m}

are connected in series. What is the effective spring constant?

Example 29

medium

A spring stores

4.5 \text{ J}

of elastic PE when stretched

0.15 \text{ m}

. Find its spring constant.

Example 30

easy

A spring has

k = 150 \text{ N/m}

. What force is needed to compress it

0.04 \text{ m}

Example 31

medium

When stretched

0.1 \text{ m}

a spring stores

0.5 \text{ J}

of energy. How much energy will it store when stretched

0.2 \text{ m}

Example 32

medium

A spring with

k = 600 \text{ N/m}

supports a

3 \text{ kg}

mass at rest. How far does it stretch from natural length? Use

g = 9.8 \text{ m/s}^2

Equilibrium stretch: x = mg/k

Example 33

easy

25 \text{ N}

pull stretches a spring by

0.05 \text{ m}

. What is the spring constant?

Example 34

medium

Three identical springs (

k = 60 \text{ N/m}

each) are arranged in parallel and support a

1.2 \text{ kg}

mass. Find the equilibrium stretch. Use

g = 9.8 \text{ m/s}^2

Example 35

hard

0.5 \text{ kg}

block slides on a frictionless surface and compresses a spring with

k = 800 \text{ N/m}

. If the block has speed

3 \text{ m/s}

at the moment it first touches the spring, find the maximum compression.

Max compression: ½mv² = ½kx²; x

Example 36

easy

A spring with

k = 50 \text{ N/m}

is compressed by

0.2 \text{ m}

. Find the magnitude of the spring force.

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Related Concepts

Force Simple Harmonic Motion Potential Energy

Background Knowledge

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

force