Practice Spring Force in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

easy

A spring with

k = 200

N/m is stretched

0.1

m. Find the magnitude of the spring force.

Example 2

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 = 20/0.5 = 40 m/s²

Example 3

medium

Two springs (

k_1 = 200

N/m,

k_2 = 200

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

Example 4

medium

A spring stretches

0.1

m under a

5

N force. How much force is needed to stretch it

0.3

Example 5

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 6

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 7

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 = 29.4/600 = 0.049 m

Example 8

easy

A spring (

k = 500

N/m) is compressed

0.04

m. Find the spring force magnitude.

Example 9

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 10

easy

A spring force of

30

N corresponds to a stretch of

0.15

m. Find the spring constant.

Example 11

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 12

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 13

easy

A spring with

k = 50 \text{ N/m}

is compressed by

0.2 \text{ m}

. Find the magnitude of the spring force.

Example 14

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 15

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 = √(mv²/k) ≈ 0.0750 m

Example 16

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 17

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 18

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?

Example 19

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 20

easy

25 \text{ N}

pull stretches a spring by

0.05 \text{ m}

. What is the spring constant?

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Force Simple Harmonic Motion Potential Energy