# mechanical energy is conserved Mechanical Energy

Conservative Forces

Conservation of Mechanical Energy

Conserved Quantities

When a quantity is conserved, it remains constant

The amount of a conserved quantity is the same at the beginning of a situation as it is at the end of the situation

Conservation of Energy

The TOTAL amount of energy in a closed system will remain constant

CLOSED SYSTEM: Nothing in or out – no interaction with the surroundings

TOTAL ENERGY: all kinds of energy

(kinetic, PE

E

, PE

G

, chemical, heat, etc.)

Mechanical Energy

Energy associated with the motion and position of everyday objects

Mechanical Energy is the sum of kinetic and potential energy

ME = KE +

PE

ME = KE + PE

G

+ PE

E

Conservation of Mechanical Energy

When there are only conservative forces acting on an object (gravity, springs),

MECHANICAL ENERGY IS CONSERVED

Conservative Forces

Conservative forces DO NOT change the amount of mechanical energy of a system

Gravity and Elastic Forces

Conservative forces will convert one form of mechanical energy into another, but the total amount of mechanical energy remains the same

Conservation of Mechanical Energy

When there are only conservative forces acting on an object (gravity, springs),

MECHANICAL ENERGY IS CONSERVED

ME i

= ME f

KE i

+ PE

Gi

+ PE

Ei

= KE f

+ PE

Gf

+ PE

Ef

Conservative Forces

Conservation of Mechanical Energy

PE

G

decreases & KE increases, but total ME remains constant (in the absence of air friction)!

Conservation of ME & Falling Objects

10000 J

5000 J

Time (s)

Conservation of ME & Pendulums

PE

G

= mgh

KE = 0

KE = ½ mv

2

PE

G

= 0

Is Mechanical Energy Conserved Here?

Nonconservative Forces

When nonconservative forces do work on a system, mechanical energy IS NOT conserved

W

NC

= ΔME

This is the

Work-Energy Theorem

Friction

Friction does negative work on the system, so the mechanical energy is decreased

While ME is not conserved when nonconservative forces (like friction) act on an object, TOTAL

ENERGY is always conserved

Total energy would include heat energy

Friction forces turn ME into non-ME (usually heat), but the total amount of energy stays the same

Friction & Pendulums