# Conservation of energy-

## 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