How much work is done by hand

Question

A mass of 20 kg compresses a spring 50 cm. The spring is then compressed an additional 2 meters by hand and then the mass and spring are released. Spring constant is 392 N/m
A)During compression process how much work was done by hand?

 For this problem, I am using

            Work=mass*gravity*(change in x) but I can't get the correct answer which is 1176 Joules 

B) when released (expanding spring) how much work is done by the spring force on the mass

     for this question how would I expand Work=F parallel)*d

 

Thank You

Answer 1

It looks like the spring-mass system is oriented horizontally, so you can ignore gravity.  You probably assumed it was oriented vertically.  

 

(A)

 

U = potential energy of spring

 

W = work done on the spring = change in potential energy of the spring

 

W = ΔU = kx₂²/2 - kx₁²/2 = (k/2)(x₂² - x₁²)

 

x₁ = compression distance at point where the hand started to do work on the spring

x₁ = 0.50 m

x₂ = compression distance at point where the hand stopped doing work on the spring

x₂ = x₁ + 2 m = 2.50 m

 

W = (392 N/m / 2)[(2.50 m)² - (0.50 m)²] = 1176 J

 

(B) 

 

To answer this, we need to know if the mass remains attached to the spring during compression by the hand, or does it remain at x₁ = 0.50 m? Let me know, so I can work part (B) for you.