Use Hooke's Law to determine the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 40 centimeters to 70 centimeters?

Work Done = 67.5 J

Explanation:

First we find the value of spring constant (k) using Hooke's Law. Hooke's is formulated as:

F = kx

where,

F = Force Applied = 450 N

k = Spring Constant = ?

x = Stretched Length = 30 cm = 0.3 m

Therefore,

450 N = k (0.3 m)

k = 450 N/0.3 m

k = 1500 N/m

Now, the formula for the work done in stretching the spring is given as:

W = (1/2) kx²

Where,

W = Work done = ?

k = 1500 N/m

x = 70 cm - 40 cm = 0.3 m

Therefore,

W = (1/2) (1500 N/m) (0.3 m) ²

W = 67.5 J