Question

A force of $20N$ is required to stretch a spring a distance of $40cm$ from its rest position. What force (in Newton) is required to stretch the same spring twice the distance?

• A. $20N$
• B. $40N$
• C. $80N$
• D. $160N$

Answer 1

The correct option is B $40N$

Force and stretch are proportional to one another such that if you double the force, the amount of stretch will double.
To stretch the spring by $x_1=40cm$, force required is $F_1=20N$

$\therefore$ Spring constant $k=\frac{F_1}{x_1}=\frac{20}{40}=0.5N/cm$

Now the spring is stretched by $x_2=2\left(40\right)=80cm$
Thus force required $F_2=k{x}_2$
$\therefore$ $F_2=0.5\times 80=40N$