Question

You are getting bored as you are stuck at home, and want to find out the effective 'spring constant' of random objects. You find a spare sock seems to stretch nice and easily. So you place a roll of quarters in your sock (approximate mass 0.23 kg) and notice that it stretches about an inch --- 2.54cm . What is the spring constant of your sock (in N/m)

Answer 1

Given Information:  

Mass of sock = 0.23 kg

Stretched length of sock = x = 2.54 cm = 0.0254 m

Required Information:  

Spring constant = k = ?

Answer:  

Spring constant = k = 88.82 N/m

Explanation:  

We know from the Hook's law that

F = kx

Where k is spring constant, F is the applied force and x is length of sock being stretched.

k = F/x

Where F is given by

F = mg

F = 0.23*9.81

F = 2.256 N

So the spring constant is

k = 2.256/0.0254

k = 88.82 N/m

Therefore, the spring constant of the sock is 88.82 N/m

Answer 2

Answer:

the spring constant of the sock = 88.74 N

Explanation:

According to Hooke's law  

F=kx

Where:

force F = mg  

k = spring constant

x =  stretching

We can say mg = kx

Making the spring constant k the subject of the formula; we have :

$k = \frac{mg}{x}$

Given that:

mass m = 0.23 kg

g = acceleration due to gravity = 9.81

x = 2.54 cm = 0.0254 m

Then plugging our values into the above derived equation; we have;

$k= \frac{0.23*9.8}{0.0254 }\\ \\ \ k = 88.74 N/m$

Thus, the spring constant of the sock = 88.74 N