# Conservation of Energy involved with a spring and two blocks and a pulley.

1. Aug 5, 2009

### Elmnt

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

Two blocks, of masses M = 2.1 kg and 2M are connected to a spring of spring constant k = 210 N/m that has one end fixed, as shown in the figure below. The horizontal surface and the pulley are frictionless, and the pulley has negligible mass. The blocks are released from rest with the spring relaxed.

(a) What is the combined kinetic energy of the two blocks when the hanging block has fallen a distance of 0.090 m?

(b) What is the kinetic energy of the hanging block when it has fallen that 0.090 m?

(c) What maximum distance does the hanging block fall before momentarily stopping?
2. Relevant equations

http://www.webassign.net/hrw/W0155-N.jpg

3. The attempt at a solution

I am not sure how to approach this problem. Initially there is no kinetic energy, however there is potential energy due to gravity from the second block. After the blocks are released .09m there is kinetic energy for the blocks and also potential energy from the spring. If I understand this correctly, the spring is doing negative work on block one and ultimately on block 2 also so it increases its potential energy. I am must be misunderstanding something somewhere. Can anyone offer a tip?

2. Aug 5, 2009

### kuruman

Don't think about the work done by the spring. Instead, concentrate on conservation of mechanical energy. When the mass comes down, the following changes occur (a) the kinetic energy of the two masses increases, (b) the potential energy of the hanging mass decreases and (c) the elastic potential energy of the spring increases. The sum of all these changes is zero,

Can you put it together?

3. Aug 5, 2009

### Elmnt

Yes! Thank you very much!