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

In summary, the hanging mass has more kinetic energy than the mass that is released, and the spring does not do any work.
  • #1
Elmnt
13
0

Homework Statement



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?

Homework Equations



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

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?
 
Physics news on Phys.org
  • #2
Elmnt said:

Homework Statement



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?

Homework Equations



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

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?

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
Yes! Thank you very much!
 

1. What is the equation for calculating potential energy in a spring-block system?

The equation for calculating potential energy in a spring-block system is PE = 1/2kx², where k is the spring constant and x is the displacement from equilibrium.

2. How does the conservation of energy apply to a spring-block system with a pulley?

The conservation of energy still applies in a spring-block system with a pulley, as the total energy (potential and kinetic) remains constant. However, the pulley may introduce some friction, causing a loss of energy in the system.

3. Can the potential energy in a spring-block system be converted into kinetic energy?

Yes, the potential energy stored in a compressed spring can be converted into kinetic energy when the spring is released and the blocks start moving.

4. How does the mass of the blocks affect the conservation of energy in a spring-block system?

The mass of the blocks does not affect the conservation of energy in a spring-block system, as long as the mass remains constant throughout the motion. The total energy will still be conserved, but the distribution of potential and kinetic energy may vary depending on the mass of the blocks.

5. What happens to the energy in the system when the spring is fully compressed?

When the spring is fully compressed, all of the potential energy in the system is converted into kinetic energy as the blocks start to move. The total energy remains constant, but the potential energy is reduced to zero while the kinetic energy is at its maximum.

Similar threads

  • Introductory Physics Homework Help
Replies
24
Views
890
  • Introductory Physics Homework Help
Replies
29
Views
822
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
408
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
30
Views
740
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
5K
Back
Top