In: Physics
A spring is compressed by 15 cm, which requires 150 N of force. What is the spring constant of the spring? How much potential energy is stored in the spring? A 20 kg box is attached to the spring. This arrangement is placed such that the spring is horizontal and the box will slide along a frictionless, horizontal track. What is the maximum speed of the box after the spring is released?
Given,
Compression, x = 15 cm = 0.15 m
Force required, F = 150 N
So,
Spring constant, k = F/x = 150/0.15
= 1000 N/m
Now,
Potential energy stored, E = 1/2*k*x2 = 0.5*1000*0.15*0.15
= 11.25 J
Now,
mass of the block, m = 20 kg
let maximum velocity attained be v
So, applying conservation of energy
=> Energy stored in spring = kinetic energy of block
=> 11.25 = 1/2*m*v2
=> 11.25 = 0.5*20*v2
=> v2 = 1.125
= 1.1 m/s