Work and Potentential Energy of a Spring

[JJBrian]

1. Homework Statement

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 don't 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.

 

[Tzim]

I think that your answer in e is correct.The energy which is stored in the spring when it is compressed becomes kinetic energy when it is released.So in equilibrium it will have the max kinetic energy.

 

[Vaal]

Problem a asks for the work done by gravity, which is a downward force. Since the object is lifted up the direction of the force is opposite the direction of the motion, which leads to negative work or -39.2J in this context. The same idea is true for c. The spring is exerting a force toward its relaxed position, but the movement is in the opposite direction leading to negative work done by the spring.

Again, if force and motion are in the same direction, the thing exerting the force does positive work. If the force and motion are in opposite directions then the thing exerting the force does negative work.

On e it looks like you have the right answer although there are a few issues with the previous step. If you are going to say the direction of the velocity is the positive direction then the value for x should be -0.1m because the spring is compressed in a direction opposite the velocity. This doesn't affect your answer because x is squared but to be technically correct you should have it in there. Also, you put in .005kg for the mass when the problem states the mass is .05kg. You still came out with the right answer so I am guessing this was just a typo.

Good luck and let me know if you have any more questions.