Work & EnergyWork & Energy

"There is nothing new to be discovered in "There is nothing new to be discovered in physics now, All that remains is more and more physics now, All that remains is more and more precise measurement.”precise measurement.”

-Lord Kelvin-Lord Kelvin

““Time is nature’s way of making certain that Time is nature’s way of making certain that everything doesn't happen all at once.”everything doesn't happen all at once.”

-Woody Allen -Woody Allen

Importance of Importance of NumbersNumbers

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Debt: 9.2 x 1012 $

Work & EnergyWork & Energy

A force is required to accelerate a body.The exertion of a force over a distance is called work. This requires energy.

W = F x dWork = Force x distance

WorkWorkCheryl Haworth lifts 297.6* lbsa distance of 2 meters.

How much work does she do?

W = F x d

d = 2 m

F = m* x a = m x g = 135 kg x 9.8 m/s2

W = F x d = m x g x d

= 135 kg x 9.8 m/s2 x 2 m

= 2657 Joules = 2657 Joules (1 Cal/4186 J)

= 0.635 Calories*A mass of 135 kg causes a gravitational force of 297.6 lbs on the surface of Earth

EnergyEnergy

• Energy is required to do work.

• The energy added to the object equals the work done.

• Energy required to move something a distance against gravity

is called gravitational potential energy

Gravitational Potential Energy: Gravitational Potential Energy:

E = W = F x d = (m x g) x h

h = height

g = * 9.82 m/s2

m = mass

* On Earth’s surface

e.g. E = 1000 m * 70 kg * 9.82 m/s2

= 6.87x105 Newton meter

Energy & Work UnitsEnergy & Work Units

Energy is measured in different units. The most common are:Energy is measured in different units. The most common are:

Joules (J) = Newton-meter (F x d)

*Calories (Cal) = 4186 J

Foot-pounds (ft-lbs) = 1.356 J

British Thermal Units (BTU) = 1055 J

Kiloton of TNT = 4.184x1012 J

• Calories with a small “c”, cal = Cal/1000.

• All foods are listed as big C calories or kilocalories (in Europe)

Potential EnergyPotential EnergyCheryl Haworth lifts 297.6* lbsa distance of 2 meters.

How much energy did the bar gain?

E = W = F x d

E = F x d = m x g x d

= 135 kg x 9.8 m/s2 x 2 m

= 2657 Joules = 2657 Joules (1 Cal/4186 J)

= 0.635 Calories

*A mass of 135 kg causes a gravitational force of 297.6 lbs on the surface of Earth

Some Kinds of EnergySome Kinds of Energy

Kinetic EnergyKinetic Energy – the energy of moving objects. This energy is: – the energy of moving objects. This energy is:

E = (1/2) m vE = (1/2) m v22

HeatHeat, or thermal energy – of warm bodies., or thermal energy – of warm bodies.

Chemical EnergyChemical Energy – of chemical reactions (involving electrons) – of chemical reactions (involving electrons)

Gravitational Potential EnergyGravitational Potential Energy – of a gravitational field. – of a gravitational field. E = m E = m

g hg h

Electromagnetic EnergyElectromagnetic Energy – energy associated with electric & – energy associated with electric &

magnetic forces.magnetic forces.

Mass EnergyMass Energy – all objects have energy by virtue of their mass, – all objects have energy by virtue of their mass,

the energy released in nuclear explosions, involving nuclei.the energy released in nuclear explosions, involving nuclei.

Why discuss Energy?Why discuss Energy?

It is transferable and conserved. It is transferable and conserved.

Kinetic EnergyKinetic Energy

E = 1/2 mv2

E = energy (Joules)m = mass (kilograms)v = speed (meters/sec.)

Florence Griffith-Joyner (born Delorez Griffith) sprints to the finish line

1 Joule = 1 kg meter2/second2

Example:

Griffith-Joyner runs 100 m in 10.61 seconds.What is her Kinetic Energy?Her mass was 60 kg and height 5’ 6’’

Kinetic EnergyKinetic Energy

E = 1/2 mv2

E = energy (Joules)m = mass (kilograms)v = speed (meters/sec.)

Florence Griffith-Joyner (born Delorez Griffith) sprints to the finish line

1 Joule = 1 kg meter2/second2

Example:

Griffith-Joyner runs 100 m in 10.61 seconds.What is her Kinetic Energy?Her mass was 60 kg and height 5’ 6’’

v = d/t = 100/10.61 = 33.93 m/sE = 0.5 * 60 kg * (33.93 m/s)2

E = 0.5 * 60 kg * (33.93 m/s)2

= 34,500 Joules = 3.4 x 104 Joules

Another Kinetic Energy Example

meters/sec14109.822adv =××==

( ) Joules492145.05.02mv2

1E =××==

A ball with mass of 0.5 kg is dropped from a distance of 10 meters. What is its kinetic energy when it hits the floor?

We know that the ball falls towards the Earth with a constant acceleration of 9.8 meters/sec2. Last class we showed that the velocity gained after traveling a distance d is given by

The kinetic energy is then

Potential Energy ExamplePotential Energy Example

A NATS102 professor lifts a ball with mass 0.5 A NATS102 professor lifts a ball with mass 0.5 kg a height of 10 meters. How much potential kg a height of 10 meters. How much potential energy does the ball gain? energy does the ball gain?

W = mah = 0.5 W = mah = 0.5 9.8 9.8 10 = 49 Joules 10 = 49 Joules

But this is the same as the kinetic energy the ball But this is the same as the kinetic energy the ball gained by falling 10 meters.gained by falling 10 meters.

What’s going on???What’s going on???

Kinetic Energy ExamplesKinetic Energy Examples

1.1. A ball with mass of 0.01 kg traveling at 100 A ball with mass of 0.01 kg traveling at 100 km/hour. What is its Kinetic Energy? km/hour. What is its Kinetic Energy?

First convert v=100 km/hour to unit of meter/sec:First convert v=100 km/hour to unit of meter/sec: Note 100 km = 100x1000 m = 100,000 m Note 100 km = 100x1000 m = 100,000 m

Note 1 hr = 3600 secondsNote 1 hr = 3600 seconds

Thus: Thus:

v=100,000 m/hour x 1hour/3600 sec=28 v=100,000 m/hour x 1hour/3600 sec=28 meters/secmeters/sec

And: And:

E = 0.5 x 0.01 x (28)E = 0.5 x 0.01 x (28)22 Joules Joules

E = 3.9 JoulesE = 3.9 Joules

A more interesting A more interesting exampleexample

2. An asteroid, 10 km=10,000 m in diameter, with a density 2. An asteroid, 10 km=10,000 m in diameter, with a density of 3000 kg/mof 3000 kg/m33, traveling at 30 km/sec. What is its Kinetic , traveling at 30 km/sec. What is its Kinetic Energy? Energy?

First: what is the asteroid’s mass? First: what is the asteroid’s mass? mass = density x volumemass = density x volumemass = density x (4/3) mass = density x (4/3) R R33

where R = radius = (1/2) diameterwhere R = radius = (1/2) diameter

Compare your answer to the energy of that Compare your answer to the energy of that of 15 kilotons of TNT, which is the energy of of 15 kilotons of TNT, which is the energy of the atomic bomb dropped on Hiroshima. the atomic bomb dropped on Hiroshima.

Mass and EnergyMass and Energy

One of Einstein’s many contributions was the One of Einstein’s many contributions was the recognition that mass is simply another form of recognition that mass is simply another form of energy. Mass and other forms of energy can be energy. Mass and other forms of energy can be interchanged, as can kinetic energy, potential energy, interchanged, as can kinetic energy, potential energy, heat, etc. The amount of energy contained in an heat, etc. The amount of energy contained in an object with mass m is given by the famous equationobject with mass m is given by the famous equation

E = mcE = mc22

where c is the speed of light. The speed of light is where c is the speed of light. The speed of light is equal to c = 3equal to c = 3101088 meters/second. meters/second.

The energy of a NATS102 StudentThe energy of a NATS102 Student

A NATS102 student has a mass of 80 kg (weight of 170 lbs). According to A NATS102 student has a mass of 80 kg (weight of 170 lbs). According to Einstein’s equation, he/she has an energy ofEinstein’s equation, he/she has an energy of

E = mcE = mc22 = 80 kg = 80 kg (3(310108 8 m/s)m/s)2 2 JoulesJoules

E = 7.2E = 7.210101818 Joules Joules

convert to kilotons of TNTconvert to kilotons of TNT

E = 7.2E = 7.210101818 J x (1 kton/4.184 J x (1 kton/4.18410101212 J) =1.7 J) =1.710101818 kilotons kilotons

This is enormous. The tremendous amount of energy contained in matter is This is enormous. The tremendous amount of energy contained in matter is the reason for the power of nuclear bombs, reactors, stars, supernovae, etc.the reason for the power of nuclear bombs, reactors, stars, supernovae, etc.

Conservation of EnergyConservation of Energy

Energy is neither created nor destroyed but only transformed Energy is neither created nor destroyed but only transformed from one form to another.from one form to another.

In a closed system, the total amount of energy is conserved. If In a closed system, the total amount of energy is conserved. If we add up the amount of energy in a closed system including we add up the amount of energy in a closed system including all of the different forms, the sum will not change with time.all of the different forms, the sum will not change with time.

The total amount of energy never changes, it only moves from The total amount of energy never changes, it only moves from place to place and from one form to another.place to place and from one form to another.

Conservation of Energy applies not just to kinetic and Conservation of Energy applies not just to kinetic and potential energy, as in the example, but to all kinds of energy potential energy, as in the example, but to all kinds of energy (heat, chemical, …)(heat, chemical, …)

Conservation Laws in PhysicsConservation Laws in Physics

Conservation laws are powerful tools Conservation laws are powerful tools Most fundamental quantities (mass, energy, & Most fundamental quantities (mass, energy, &

momentum) satisfy conservation laws.momentum) satisfy conservation laws. Conservation laws are easy – no vectorsConservation laws are easy – no vectors

Conservation of EnergyConservation of Energy

m = 50.9 kg

PowerPowerThe rate of doing work or expending energy

P = Energy/Time

Rock climbers gain a lot of potential energy but do so slowly, at low power

Power Power TrainingTraining

Cyclists do work Cyclists do work more quickly than more quickly than rock climbers. They rock climbers. They expend more expend more power.power.

Lance Armstrong Lance Armstrong expends about expends about 10,000 Calories in 10,000 Calories in

a 2 hour race. This a 2 hour race. This corresponds to a corresponds to a power of roughly 6 power of roughly 6 kilowatts. kilowatts. Lance training in Arizona

Racing: Tour de France

Niagara FallsNiagara Falls

570,000 kg of water descend every 570,000 kg of water descend every second.second.

The falls height is 55 meters. The falls height is 55 meters.

Thus the potential energy of 1 kg of Thus the potential energy of 1 kg of water is E=mha=1water is E=mha=19.89.855 J = 539 J.55 J = 539 J.

The total power is thenThe total power is thenP=570,000P=570,000539 Joules/sec=3.1539 Joules/sec=3.1101088 WattsWattsor 310 Megawatts.or 310 Megawatts.

Climbing out of the Grand Climbing out of the Grand CanyonCanyon

How big a lunch is needed?How big a lunch is needed?Energy from lunch = Energy from lunch = Work to be doneWork to be done

W = mghW = mgh= (62 kg)(9.82m/s= (62 kg)(9.82m/s22)(1500 )(1500 m)m)= 9.1x10= 9.1x1055 Joules Joules

= 218 Calories = 218 Calories

That is, That is, 1 peach & a glass of milk 1 peach & a glass of milk

That’s it?That’s it?

Nope – we’re inefficientNope – we’re inefficient

Humans work at roughly Humans work at roughly 15% efficiency. The rest of 15% efficiency. The rest of the energy goes into heat the energy goes into heat and non-work productive and non-work productive movement. movement.

So, to climb the Grand So, to climb the Grand Canyon, we need 1450 Cal Canyon, we need 1450 Cal ! !

Two club sandwiches, one Two club sandwiches, one egg, 1 fruit and 1 glass of egg, 1 fruit and 1 glass of milk. milk.

A more interesting A more interesting exampleexample

2. An asteroid, 10 km=10,000 m in diameter, with a density 2. An asteroid, 10 km=10,000 m in diameter, with a density of 3000 kg/mof 3000 kg/m33, traveling at 30 km/sec. What is its Kinetic , traveling at 30 km/sec. What is its Kinetic Energy? Energy?

First: what is the asteroid’s mass? First: what is the asteroid’s mass? mass = density x volumemass = density x volumemass = density x (4/3) mass = density x (4/3) R R33

v=30 km/sec = 30,000 meters/secv=30 km/sec = 30,000 meters/secE = 0.5 x 1x10E = 0.5 x 1x101313 x (30,000) x (30,000)2 2 JoulesJoulesE = 4.5x10E = 4.5x102121 Joules Joules

Convert to kilotons of TNTConvert to kilotons of TNTE = 4.5x10E = 4.5x102121 Joules x (1 kiloton/4.184x10 Joules x (1 kiloton/4.184x101212

Joules)Joules)E = 2.2x10E = 2.2x1088 kilotons of TNT kilotons of TNT

The atomic bomb dropped on Hiroshima released and The atomic bomb dropped on Hiroshima released and energy of 15 kilotonsenergy of 15 kilotons