Energy

Energy is the ability to do work. Thus, energy is the ability to make something move.

Energy can be classified as potential or kinetic. 

Potential energy is stored energy.  Ex: chemical energy stored in a match

head or in a battery, mechanical energy stored in a stretched rubber band. 

Kinetic energy is the energy of motion.  Ex: A ball in flight, a vibrating molecule, a

hammer hitting a nail.

The Law of Conservation of Energy states that energy cannot be made or destroyed, but only transferred from object to object and changed in form.

If you strike a match its chemical potential energy is transformed into heat and light energy.

The chemical energy in a flashlight battery can be converted to electrical energy, which a motor can then convert to mechanical energy to move a toy.

A stretched rubber band, when released, will convert its potential energy into the kinetic energy that shoots a slingshot.  

Moving air and running water have mechanical kinetic energy that can be transferred to windmills and turbines, which spin generators that convert the mechanical energy to electrical energy. 

In all of these changes, exactly the same amount of energy is present after

the change as was present at the start.  The energy may be in a different form,

however, and may be in different objects.

SO:• Moving objects have kinetic energy.• Objects that have energy because of

position have potential energy.• Work is the transfer of energy.

A derivation for kinetic energyVf

2 = Vi2 + 2ad

If Vi = 0m/s, Vf

2 = 02 + 2adIf we check at any particular instant, Vf = v , So v2 = 2ad we can rearrange that to say d = v2

2a

Let’s look at work. If W = Fd and F = ma then

W = mad and we substitute from above for “d”

W = mav2 cancel “a” 2a

Ek = mv2 is the formula for kinetic energy.

2

An object needs work done on it to give it Ek.

Therefore, work done is equal to change in energy.

Net Work = mv2 _ mv’2

2 2

A .145kg baseball is thrown with a speed of

25m/s .What is it’s kinetic energy?Ek = ½ (.145)(25)2

= 45JHow much work was done to reach this speed

from rest?W = mv2 _ mv’2

2 2W = (.145)(25)2 _ (.145)(0)2 = 45J

2 2

How much work is required to accelerate a 1000kg car from

20m/s to 30m/s?The work needed is equal to the

increase in kinetic energy.W = mv2 _ mv’2

2 2 = (1000)(30)2 – (1000)(20)2

2 2 = 250000J

A derivation for potential energy

Vf2 = Vi

2 + 2ad where a = accel due to gravity

Vf2 = Vi

2 + 2gd where d = height

Vf2 = Vi

2 + 2gh multiply by m/2

mVf2 = mVi

2 + m2gh at one instant Vf = Vi

2 2 2 mV2 = mV2 + mgh 2 2 Ep = mgh is the formula for

gravitational potential energy

A .400kg ball on a 75.0m high cliff has…

Ep = mgh

=(.400)(9.8)(75)=294J of

gravitational potential energy

Ek = mv2

2=(.400)(0)2

2= 0J of kinetic

energy

When that ball has fallen 25.0m…

Ep = mgh

=(.400)(9.8)(50)=196J of

gravitational potential energy

Vf2 = Vi

2 + 2ad

Vf2 = 02 + 2(9.8)(25)

Vf = 22.1m/s

Ek = mv2

2=(.400)(22.1)2

2= 98J of kinetic

energy

When that ball has fallen 75.0m…

Ep = mgh

=(.400)(9.8)(0)=0J of

gravitational potential energy

Vf2 = Vi

2 + 2ad

Vf2 = 02 + 2(9.8)(75)

Vf = 38.3m/s

Ek = mv2

2=(.400)(38.3)2

2= 294J of kinetic

energy

Wait a minute!

At 75.0m high, Ek = 0J and Ep =294J

At 50.0m high, Ek = 98J and Ep

=196JAt 0m high, Ek = 294J and Ep =0J

The total energy is 294J at all times!

Energy is conserved.