Question

A spring with a force constant of 4.0×10⁴ N/m is initially at its equilibrium length. How much work must you do to stretch the spring 0.030 m ? How much work must you do to compress the spring 0.030 m ?

Answer 1

The work done to stretch or compress a spring can be calculated using the formula (1/2)kx^2, where k is the force constant of the spring and x is the displacement. For an initial displacement of 0.030 m, the work done would be 18 J.

Step-by-step explanation:

To calculate the work done to stretch or compress a spring, we can use the formula:

Work = (1/2)kx^2

where k is the force constant of the spring and x is the displacement from the equilibrium position.

For stretching the spring by 0.030 m, the work can be calculated as:

Work = (1/2)(4.0×10^4 N/m)(0.030m)^2 = 18 J

For compressing the spring by 0.030 m, the work would also be 18 J since the formula only depends on the displacement and the force constant and is independent of the direction of displacement.