Use Hooke's Law to determine the work done by 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 50 centimeters to 80 centimeters

Hooke's law states that the force applied to an elastic material is directly proportional to its extension, provided its elastic limit is not exceeded.

To calculate the amount of work done by Hooke's law, first, we need to find the force constant of the spring.

Formula:

F = ke................. Equation 1

Where:

F = Force applied
k = Spring constant
e = extension

make k the subject of the equation

k = F/e................ Equation 2

From the question,

Given:

F = 450 N
e = 30 cm = 0.3 m

Substitute these values into equation 2

k = 450/0.3
k = 1500 N/m.

Finally, To find the work done in stretching the spring from 50 cm to 80 cm, we use the formula below.

W = ke²/2........... Equation 3

Where:

W = Work done
k = spring constant
e = extension

Also, From the question,

Given:

e = (80-50) = 30 cm = 0.3 m
k = 1500 N/m

Substitute these values into equation 3

W = 1500(0.3²)/2
W = 67.5 J.

Hence, The work done in stretching the spring from 50 cm to 80 cm is 67.5 J.

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