Energy stored in a Stretched String

When stretching a rubber band or a spring, the more we stretch it the bigger the force we must

apply.

Hooke’s Law

• For an ideal string we that to double the stretch we must double the force.

• Hooke’s Law states – For an ideal spring the extension or compression is proportional to the force producing it

• F = k x• Where x is the extension or compression

of the spring.• K is called the spring constant

• For a spring, a graph of Force against extension will produce a straight line of gradient k which passes through the origin.

ForceF

Extension x

Gradient = k

Example

• A spring of length 10cm is extended to 15cm when a 1kg mass hangs from it. Find k

X = 15cm – 10cm = 5cm = 0.05m

F = mg = 1kg x 10ms-2

= 10 N

F = k x

K = F / X

= 10 / 0.05 = 200 Nm-1