WORK & ENERGYAP Physics C: Mechanics

What is Energy?What is its definition?

What are its properties?

What forms can it be in?

The ability of a physical system to cause change

Energy can come in many forms and is transferrable. It is a

conserved quantity in the universe.

Chemical, electrical, nuclear,

thermodynamic, light, mechanical, kinetic,

potential, elastic, etc.

What is Work?What is its definition?

What are its properties?

How can it be calculated?

The amount of energy transferred by a force

acting through a displacement

Work (Energy) is a scalar quantity.

W=fscosθ

Work

W Fscos

W F s

The area under an Force-displacement graph

W Fx dx

WorkWork is an energy transfer.

If energy is added to the system then W is positive.

If energy is transferred from the system then W is negative.

WorkWork is a scalar.

The NET work on an object is the sum of the work done by each force acting on it.

WorkUnits of work

System Unit Alternate name

SI Nm Joule (J)

cgs dyne*cm erg

English foot*pound -

1 erg=10-7J

Work-Energy Theorem

W 12

mv2 KE

W 12

mvf2 1

2mvi

2

The work done by a net force in displacing a particle equals the

change in kinetic energy of the particle. Stress on the word particle. This is

a drastic idealization.

Mechanical Potential Energy Gravitational

Elastic

E g mgh

E las 12

kx2

Conservation of EnergyThis is always true, but mechanical energy is only

conserved when only conservative forces are present.

Work done by a conservative force is path independent

Forces such as friction and air drag are non-conservative. They result in energy dissipated as heat.

What is it?

PowerThe time rate at which work is being done.

P Wt

How do we calculate it?

If a net force acts on a particle and does work W over an interval of time Δt, then the average power is:

Power The time rate of energy transfer.

P dWdt

Instantaneous Power

W F ds

dW F ds

dWdt

F dsdt

P F v

Power Watt are the units?

JouleSecond

Kgm2

s3

Watt

1hp=550ft*lbs/sec=746W

Note: A kilowatt-hour is often used by power companies. What is it a measure of?

Potential Energy and Conservative Forces

Potential energy is only associated with conservative forces. If an object or field does work on some external object, energy is transferred from

the object or field to the external object:

The energy transferred as work decreases the potential energy of the system from which it came.

Fx dx U

Potential Energy and Conservative Forces

The conservative force equals the negative (partial) derivative of the potential energy with respect to x.

The negative sign means that the final potential energy of the system is lower than the initial as the

conservative force does work.

Fx dUdx

Potential Energy and Conservative Forces

Examples:

Fs dUdx

d 1

2kx2

dx kx

Fg dUdy

dmgy

dy mg

E mc2