Question

A spring scale hung from the ceiling stretches by 6.1 cm when a 2.0 kg mass is hung from it. The 2.0 kg mass is removed and replaced with a 2.5 kg mass.
Part A What is the stretch of the spring?

Answer 1

To solve this problem, we need to use Hooke's Law. 

Hooke's Law: 

F = -kx

where F = mg
m = mass of the object
g = gravitational force
k = spring constant
x = length of stretch of the spring

Solve for the spring constant, k:

2.0 kg * 9.81 m/s^2 = -k*(6.1cm/100cm/m)

k = 321.64 

The stretch of the spring with mass of 2.5 kg is then determined: 

2.5 kg * 9.81 m/s^2 = -321.64 *(x)
x = 7.62 cm