Find, using integration, the work done in compressing a spring by a distance x.

[integral from 0 to x']dW= [integral from 0 to x'] F(x') dx'

=[integral from 0 to x']kx' dx'

=1/2kx^2
It is a 1-D problem so line integral do not need to be used. At a given instant, let the amount by which the spring is already compressed be x'. The force in the spring is then F = kx', where k is the spring constant. This means if we compress the spring further by an infinitesimal dx, the work done is dW given by dW = kx' dx.
So it is possible to integrate to find the work done from x = 0 to x = x'.

Answered by Matteo T. Physics tutor

2867 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

A car is travelling at 10m/s when it brakes and decelerates at 2ms^-2 to a stop. How long does the car take to stop?


Draw the electric field lines produced by a negative point charge and calculate the electric field strength at a distance of 50mm from a point charge of size -30nC.


Explain Newton’s law of Gravitation


Explain why a transformer is used in electrical power lines.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences