Question

if it takes 4J work to stretch a hooke's law spring 10 cm from its equilibrium length, determine the extra work required to stretch it an additional 10 cm

Answer 1

12 J

Step-by-step explanation:

The amount of energy stored in a spring stretched by a distance x is:

E = 1/2 k x², where k is the stiffness of the spring.

So the spring has 4J of energy when it is stretched 10 cm:

4 J = 1/2 k (0.10 m)²

k = 800 N/m

When the stretched to 20 cm, the amount of energy is:

E = 1/2 (800 N/m) (0.20 m)²

E = 16 J

So it takes an additional 12 J to stretch the spring an additional 10 cm.