What is Energy?

• The ability to do work– The ability to create a change

• Energy comes in many forms– Mechanical

• Potential • Kinetic

– Electrical– Thermal– Nuclear– Chemical

• It can be transformed from one form to another• Like work, it is measured in Joules

Mechanical Energy• Deals with the energy an object has because of

either it’s motion (kinetic energy), and/or the outside forces acting on the object trying to make it move (potential energy)

• A car moving at 50 mph can do a lot of damage to a pedestrian if they hit--this is because of the car’s motion.

• On the other hand, a 16 pound bowling ball being held 10 ft above a person’s head (but not moving) can be dangerous, because the force due to gravity pulls down on the ball. The ball has the potential to fall on the person’s head. The ball is not falling, BUT IT COULD because of the force of gravity.

Potential Energy• Energy that is not being applied to the object’s

motion, BUT IT COULD BE LATER ON.• It is the work done by something, other than you

(such as gravity), naturally on its own.– Gravity causing things to fall– Attraction/repulsion of electrical charges– Expansion/contraction of a spring

• Potential energy depends on the position and condition of the object (the forces that act on it).

• Think of a stretched rubber band on a slingshot. It has potential energy due to its position. If the rubber band is released, it is capable of doing work.

• Some call potential energy “stored energy” but that term is very misleading (the energy does not come from the object).

Gravitational Potential Energy

• Potential Energy due to gravity (Epg).– Gravity is always trying to do work on objects by

pulling them down to the ground.• Epg of an object is equal to the work done by

gravity to make an object fall.• Work = Force*distance• Workgravity = Forcegravity* distance dropped = mag(-h)• Since ag = -9.8 m/s/s we use g. (g = 9.8 m/s/s)

• Epg = mgh • Gravitational potential energy = /Fg/ * height

Calculating Epg

• Calculate the change in potential energy of 8 million kilograms of water dropping 50 m over Niagara Falls.

• Know: m= 8 million kg h = 50 m

g = 9.8 m/s2

• EPg = mgh =(8,000,000 kg)(9.8 m/s2)(50 m) = 3,920,000,000 J or 3.92

x109 J

Elastic Potential Energy

• Since a compressed spring wants to expand, and is willing to do work on any object in the way of its expansion, we call the work done by a spring the elastic potential energy (Epel).

• This is also true for a stretched spring. It wants to contract back to its original length, and will pull anything attached to it.

• Some people call the elastic potential energy of a spring the potential energy of a spring (Eps).

• elastic potential energy (Epel) is a more general name.

• (Eps) = work of a spring = (1/2)k(Dx)2

Kinetic Energy

• Energy of motion– It is the energy an object has BECAUSE it is

moving. It IS NOT, IN ANY WAY, BY NO MEANS the energy an object uses to keep moving. (REMEMBER INERTIA).

• Depends on the mass and velocity of the object.• Kinetic energy = (½)(mass)(velocity)2

Ek = (½)mv2

• Notice an object’s velocity has a greater impact on its kinetic energy than it’s mass.

Work - Energy Theorem

• The work done on an object is defined as the change in that object’s energy.

• Work = Change in Ep + Change in Ek

• W = DEp+ DEk

Work - Energy Theorem

• A moving object is capable of doing work.– It can lose some of it’s kinetic energy (slow down) and

create a change on another object in the process.– Car hitting an object– A bat hitting a ball– Electrical charges moving through a wire– Hot steam moving the turbines of an electrical generator

• An object can also convert it’s potential energy into kinetic energy so that it can do work.

Work

Potential EnergyKinetic Energy

Net Work

• This is the overall work done on an object• The net work is done by the net force acting on an

object• The net work always equals the change in kinetic

energy• Fnet//d = (1/2) mvf

2 - (1/2) mvi2

• Objects in equilibrium never have any net work done on them

• Fnet = 0 N

• Objects that move with a constant speed, never have any net work done on them.

A quick comparisonObjects A and B are initially sliding on smooth ice and come to arough surface. Object A slides a distance of D as it comes to a stop.How far (in terms of D) will object B have to slide to also come to a stop? (The coefficient of kinetic friction is the same for both boxes.)

mA

mB

VA

VB = 2VA

mA

Rest

DSince object B has twice thevelocity of A it has 4X theEK. This means friction must do 4X the work on B than on A.

And since the masses of A and B are the same, they both have the same frictional force. So object B must slide 4X farther than object A to do all that work. This is why you should never speed when driving.

Another comparisonObjects A and B are initially sliding on smooth ice and come arough surface. Object A slides a distance of D as it comes to a stop.How far (in terms of D) will object B have to slide to also come to a stop? (The coefficient of kinetic friction is the same for both boxes.)

mA

mB = 2mA

VA

VB = VA

mA

Rest

DSince object B has 2X themass of object A, it has 2X theEK of A. This means friction must do 2X the work on B than on A.

Because Object B has 2X the mass of object A it also has 2X the frictional force of object A. So object B slides the same distance as object A.

Conservative forces.• Some forces (such as gravity and electrical forces)

convert the work needed to overcome them, into potential energy. This means that the energy you used to move an object can be given back later on.

• For example, you do 30 joules of work to lift a block (you had to fight gravity to lift it). The block now has 30 joules of gravitational potential energy that can be used later on.

• Gravity is called a CONSERVATIVE FORCE. These forces conserve the amount of mechanical energy in a system.

• They convert EK into EP and vice versa. Conservation means to save. The total energy in a conservative system is a constant.

Non-conservative forces• Other forces, such as friction, convert the work

done on an object into heat.• Heat is a form of energy, but not one we can ever

use again. Thus some say that the energy is “lost”.• You push a block across a rough floor. Once it

stops moving, it does not return on its own to the starting point.

• Non-conservative forces often create heat--they do not keep the amount of mechanical energy of a system constant.

• Work = Change in Ep + Change in Ek + Heat(if any)• W = DEp+ DEk + Q (if any)

Law of Conservation of Energy• It states: Energy cannot be created nor

destroyed. It is transformed from one form into another, but the total amount of energy never changes.

• Example - when gasoline combines with oxygen in a car’s engine, the chemical Ep of the fuel is converted to molecular Ek, and thermal energy. Some of this energy is transferred to the piston and some of this energy causes the motion of the car. The rest of the energy escapes (“is lost”) the system of the engine (as heat) and enters the environment.

• “Lost energy” is not energy that is destroyed, it is simply energy we cannot use.

Application of the Conservation of Energy

• If there are only conservative forces acting on a system then we can say:– The starting total mechanical energy = the final mechanical energy

• ETi = ETf

• Epi + Eki = Epf + Ekf

• The conservation of energy simplifies many complex problems into one easy process.

Sample problem 1• A block is released from rest at the top of a

smooth incline and slides to the bottom. What is the block’s final speed when it reaches the bottom?

5 m

5 m

0 m

Epgi = mass(9.8m/s/s)(5m) Epgf = mass(9.8m/s/s)(0m)

Eki = (1/2)mass(0 m/s)2 Ekf = (1/2)mass(Vf)2

ETi = mass(9.8m/s/s)(5m) ETf = (1/2)mass(Vf)2

mass(9.8m/s/s)(5m) = (1/2)mass(Vf)2

2(9.8m/s/s)(5m) = Vf

Vf

Ep EK Ep EK Ep EK

The total energy atone point is thesame for all pointsfor a conservativesystem

Start Middle End

Sample problem 2

• A ball held from a height of 5 meters is dropped. What is the speed of the ball when it hits the ground?

5 m

5 m

0 m

Epgi = mass(9.8m/s/s)(5m) Epgf = mass(9.8m/s/s)(0m)

Eki = (1/2)mass(0 m/s)2 Ekf = (1/2)mass(Vf)2

ETi = mass(9.8m/s/s)(5m) ETf = (1/2)mass(Vf)2

mass(9.8m/s/s)(5m) = (1/2)mass(Vf)2

2(9.8m/s/s)(5m) = Vf

Vf

Independence of Path

• When a system is conservative, the path the object takes to go from point A to point B has no impact (is independent of) …

• The work needed to go there• The change in Ep

• The change in Ek