GCSEPhysics: Combined ScienceWJECRevision NotesForces, Space & RadioactivityWork & EnergyCalculating Work Done in Stretching

Calculating Work Done in Stretching (WJEC GCSE Physics: Combined Science)

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Ann H

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Ann H

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Calculating Work Done in Stretching

  • When a spring is stretched by a force work is done by the spring
  • The work done in stretching a spring is equal to the elastic energy stored in the spring

Work Done in Stretching a Spring

2-3-stretched-spring

Work is done on a spring when it is stretched

  • Work done is calculated using the equation:

W space equals space 1 half F x

  • Where:
    • W  = work done by the spring or elastic potential energy (J)
    • F = force applied to stretch the spring (N)
    • x = extension of the spring (m)
  • This is only valid for springs not stretched beyond their limit of proportionality 

Calculating Work Done from the Force-Extension Graph

  • Work done is calculated from the area under a force-extension graph
  • The area under the graph forms a triangle shape
    • Where the area of a triangle is 1 half space cross times space base space cross times space height
  • So, the work done = area = 1 half space cross times space extension space cross times space force

Area Under a Force-Extension Graph

2-3-area-under-force-extension-graph

The area under the force-extension graph is a triangle. Calculating the area of the triangle gives the work done by the spring when stretched

Worked example

A 250 g mass is attached to the bottom of a hanging spring. It stretches from 10.0 cm to 11.4 cm. 

Gravitational field strength = 10 N/kg

Calculate the elastic potential energy stored by the stretched spring.

Answer

Step 1: Draw a diagram of the situation

Extension Worked Example, downloadable IGCSE & GCSE Physics revision notes

Step 2: List the known quantities

  • Mass added, m = 250 g
  • Original length = 10.0 cm
  • Final length = 11.4 cm
  • Gravitational field strength = 10 N/kg

Step 3: Determine the extension of the spring in m

  • There are 100 cm in 1 m

extension, x = final length − original length

x = 11.4 − 10.0 cm

x = 1.4 cm

x = 1.4 ÷ 100 = 0.014 m

Step 4: Determine the force on the spring

Weight =  F = mg

F = 250 × 10 

F = 2500 N 

Step 5: Recall the equation for work done

W space equals space 1 half F x

Step 6: Calculate the work done

W space equals space 1 half space cross times space 2500 space cross times space 0.014

bold italic W bold space bold equals bold space bold 17 bold. bold 5 J

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    Ann H

    Author: Ann H

    Expertise: Physics

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.