Answer:
The potential energy (P.E.) stored in an elastic spring is equal to the work done in compressing or stretching the spring.
When a spring is compressed or stretched, the force required to do so is given by Hooke's law, which states that the force F required to compress or stretch a spring by an amount x is given by
F = kx, where k is the spring constant.
The work done in compressing or stretching a spring is equal to the force required to do so multiplied by the distance over which the force is applied.
In the case of a spring, this distance is equal to the amount x by which the spring is compressed or stretched.
Therefore, the work done in compressing or stretching a spring is given by
W = Fd = kx * x = kx^2.
The potential energy stored in the spring is equal to the work done to compress or stretch it.
Therefore, the potential energy of a spring that is compressed by an amount x is given by P.E. = W = kx^2.
Substituting kx^2 = 1/2 kx^2, we find that
P.E. = 1/2 kx^2.
This shows that the potential energy stored in an elastic spring is equal to 1/2 times the spring constant multiplied by the amount x by which the spring is compressed or stretched.
Step-by-step explanation: