Question

A 150kg person stands on a compression spring with spring constant 10000n/m and nominal length of 0.50.what is the total length of the loaded spring

Answer 1

The total length of the spring would be 0.65 m

Step-by-step explanation:

The Concept

Hooke's law evaluates the increment of spring in relation to the force acting on the body. 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

Step by Step Calculations

We have to obtain x before adding it to the nominal length, We make 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/
`s^(2)`

k is the spring constant = 10000 N/m

then x = (9.81 m/
`s^(2)` 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 = 0.14715 m + 0.5 m = 0.64715

L ≈ 0.65 m

Therefore the total length of the spring would be 0.65 m