What is the spring constant? On what factors does the work done by a spring depend?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The spring constant $(k)$ is a measure of the stiffness of a spring. It is defined as the force required to produce a unit extension or compression in the spring. According to Hooke's Law,$F = -kx$,where $F$ is the restoring force,$x$ is the displacement from the mean position,and $k$ is the spring constant. Its $SI$ unit is $N/m$.
The work done by a spring when it is displaced from position $x_1$ to $x_2$ is given by the formula: $W = -\frac{1}{2} k (x_2^2 - x_1^2)$.
From this expression,we can conclude that the work done by a spring depends on:
$1$. The spring constant $(k)$,which represents the stiffness of the spring.
$2$. The initial position $(x_1)$ of the spring.
$3$. The final position $(x_2)$ of the spring.

Explore More

Similar Questions

$A$ spring $40 \, mm$ long is stretched by the application of a force. If $10 \, N$ force is required to stretch the spring by $1 \, mm$,then the work done in stretching the spring by $40 \, mm$ is ............. $J$.

$A$ body of mass $0.15 \ kg$ moving with a velocity of $15 \ ms^{-1}$ comes to rest when it hits a spring that is fixed at the other end. If the force constant of the spring is $1500 \ Nm^{-1}$,then the compression in the spring is: (in $m$)

$A$ spring has a spring constant $200 \,N/m$. If it is stretched by $1 \,cm$, then the potential energy stored in it is: (in $\,J$)

When a body of mass $m$ is attached to a vertical spring of natural length $L$ and released,the spring stretches by a distance $h$. What will be the potential energy of the stretched spring?

$A$ spring has a natural length $l$ with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance $l$ below the ceiling. Initially,the spring makes an angle of $60^{\circ}$ with the vertical,when the system is released from rest. Find the angle of the spring with the vertical,when the velocity of the ring reaches half of the maximum velocity,which the ring can attain during the motion.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo