# Work/Potential Energy of a Spring

1. Nov 8, 2009

### JJBrian

1. The problem statement, all variables and given/known data

a)how much work is done by gravity as a 2kg mass is raised 2m vertically?

b)what is the change in gravitation potential energy of a 2kg mass raised 2m vertically?

c)How much work is done by a spring with a spring constant k = 50N/m as it is compressed by 0.1m from its relaxed position?

d) what is the change in the potential energy of a spring with spring constant k = 50N/m as it is compressed by0.1m from is relaxed position?

e) A 0.05kg mass is held against a spring( with spring constant k = 50N/m) while the spring is compressed by 0.1m. The mass is released and accelerated by the spring. What is the final speed of the mass?

3. The attempt at a solution

A. Wg= mgh wg = (2)(9.8)(2) = 39.2J
B. PE = mgh PE = (2)(9.8)(2) = 39.2J
C. Ws = 1/2kx^2 Ws = 1/2(50)(.1)^2 = 0.25J
D. Us = 1/2 kx^2 Us = 1/2(50)(.1)^2 = 0.25J
E. I dont know....
W = change KE
attempt 1/2kx^2 = 1/2mv^2
1/2(50)(.1)^2 = 1/2(.005)v^2
vf = sqrt(10)m/s

can someone check my work?
I need some help and explanation for problem e.
Im not too sure about the signs.

2. Nov 10, 2009

### gabbagabbahey

You seem to be missing a few negative signs...It might help you to find them by looking at the definition of work done by any force $\textbf{F}$ in moving an object form point $\textbf{a}$ to point $\textbf{b}$...what is that definition (it involves an integral and a dot product)?