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

the spring constant of the sock = 88.74 N

Step-by-step 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 = (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= (0.23*9.8)/(0.0254 )\\ \\ \ k = 88.74 N/m`

Thus, the spring constant of the sock = 88.74 N

Answer 2

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