Problem 1: A 150 kg person stands on a compression spring with spring constant 10,000 N/m and nominal length of 0.50. What is the total length of the loaded spring?

The total length of the spring is 0.65 m

Explanation:

Hooke's Law

Hooke's law is use to determine the increment of a spring that is acted upon by a force which is either compression or expansion. Hooke's law states that for a spring undergoing deformation, the force applied is directly proportional to the deformation experienced by the spring. Hooke's law is represented thus;

F = k x ... 1

where F is the force applied to the spring

k is the spring constant

x is the spring stretch or extension

Calculations

The extension x can be obtained by making x the subject formula in equation 1;

x = F/k

but F = m x g

so, x = (m x g) / k

given that, the mass of the person m = 150 kg

g is the acceleration due to gravity = 9.81 m/

k is the spring constant = 10000 N/m

then x = (9.81 m / x 150 kg) / 10000 N/m

x = 0.14715 m

the extension experienced by the spring after the compression is

0.14715 m

The total length of the spring would be;

L = extension + nominal length

L = 0.14715 m + 0.5 m = 0.64715

L ≈ 0.65 m

Therefore the total length of the spring would be 0.65 m