Is Energy Conserved in Vertical and Horizontal Spring-Mass Systems?

[noleguy33]

Homework Statement

Part 1: A mass is hung from a spring that is vertical. The mass is made to oscillate vertically. Call the initial time when the mass is at its highest position and the final time when the mass is at its equilibrium position.

Part 2: A mass on a table is attached to spring that is horizontal. You give the mass a brief push so that the mass travels horizontally. Call the initial time when the spring first reaches its maximum stretch in the initial direction of motion. The final time is when the spring first reaches its zero stretch length.

The question is, is energy conserved for the following systems-

Part 1 - Mass, Mass+earth, Mass+earth+spring
Part 2 - All combinations of mass, the table and the spring.

Homework Equations

Work energy theorem - Wsys = ΔKE + ΔThermal + ΔUgrav + ΔUspring +ΔEother

Energy in - Energy out = ΔEsys

The Attempt at a Solution

I'm working through each system and here is what I've come up with-

Part 1. In each case, energy is converted from PE to KE, so it should always be conserved

Part 2.
mass+spring+table: Energy is conserved because thermal energy will stay within the system
mass+spring: Not conserved because part of the mass's KE will be converted to thermal
mass+table: conserved because thermal energy will be split between the two.
mass: not conserved due to loss of thermal energy
table: conserved because no work is being done on the table

Thanks in advance.

 

[anathema]

Thank you for your post. I would like to offer some feedback on your solutions for Part 1 and Part 2 of the problem.

Part 1:
You are correct in saying that energy is conserved in all three systems. However, I would like to add that in the case of the mass+earth+spring system, the gravitational potential energy of the mass is also converted into kinetic energy as it oscillates. So, in addition to the conversion of spring potential energy into kinetic energy, there is also a conversion of gravitational potential energy into kinetic energy. This means that the total energy (kinetic + potential) remains constant and is conserved.

Part 2:
In the system of mass+spring+table, you mention that thermal energy will stay within the system and therefore energy is conserved. While this is true, I would like to point out that in this system, there is also an external force (the push) acting on the mass, which does work on the mass and increases its kinetic energy. So, in this case, energy is conserved because the external work done on the system is equal to the change in kinetic energy of the mass.

In the system of mass+spring, you mention that energy is not conserved because part of the mass's kinetic energy is converted into thermal energy. This is correct, but I would like to clarify that energy is still conserved within the system (mass + spring) itself. The conversion of kinetic energy into thermal energy is a result of internal forces within the system, and the total energy within the system remains constant.

For the system of mass+table, you mention that energy is conserved because thermal energy will be split between the two. Again, this is correct, but I would also like to add that in this system, there is no external work being done on the system, so the total energy (kinetic + potential + thermal) remains constant.

Lastly, for the mass and table systems, you mention that energy is not conserved due to the loss of thermal energy. This is not entirely accurate. While there may be a loss of thermal energy, energy is still conserved within the system itself. However, since there is an external force (the push) acting on the mass, energy is not conserved for the entire system (mass + external force).

I hope this helps clarify the concept of energy conservation in these systems. Always remember to consider all