Hooke's law states that the force required to stretch or compress a spring to x units longer or shorter than its natural length is, for sufficiently small values of x, proportional to x. That is, F(x) = kx for some constant k, called the spring constant. Suppose that a force of 10 N is required to stretch a spring by 5 cm. Find the work done in stretching the spring that far.
A) 25 N . cm
B) 22 N . cm
C) 27 N . cm
D) 29 N . cm
E) 20 N . cm

Question

Quizplus · Accepted Answer

The work done in stretching the spring is calculated using the formula $W = \frac{1}{2}kx^2$. Given $F(x) = kx = 10$ N when $x = 5$ cm, we first find $k = \frac{F}{x} = \frac{10}{5} = 2$ N/cm. Then, $W = \frac{1}{2} \cdot 2 \cdot 5^2 = 25$ N·cm.

Hooke's Law States That the Force Required to Stretch or Compress