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

3448 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is the angular speed of a car wheel of diameter 0.400m when the speed of the car is 108km/h?


An object with weight w is suspended from two strings at angles θ1 and θ2 to the vertical and with tensions T1 and T2. How would you resolve the vertical and horizontal forces?


A hot air balloon is travelling at a speed of 5.0m/s at an angle of 60.0 degrees up from the horizontal. Find the vertical and horizontal components.


Show that a mass on a spring obeys simple harmonic motion.


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences