2023 Work, Energy and PowerPotential Energy of a Spring Easy Question 1 of 7 in Potential Energy of a Spring

The potential energy of a long spring when stretched by 2 cm is $U$. If the spring is stretched by 8 cm, potential energy stored in it will be:

A $16U$
B $2U$
C $4U$
D $8U$

The answer is A.

Solution

Spring PE is $\frac{1}{2}kx^2$, so 4 times the stretch gives $16U$.

Potential energy stored in the spring $=\frac{1}{2}kx^2$ Now $\frac{1}{2}k(2)^2=U$ and $\frac{1}{2}k(8)^2=U'$ (say) $\Rightarrow U'=\frac{64}{4}U=16U$

Concept elastic potential energy ∝ x²

Potential Energy of a Spring in past papers

7 questions from this chapter have appeared across 7 exam years.