Work & Energy

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

-Lord Kelvin

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

-Woody Allen

Forces are vectors

You can consider perpendicular motion independently.

F=ma means: Fx(total) = max

Fy(total) = may

or: F(total) = ma

y

x Fy

Fx

F

Energy: Main Points

• Energy comes in different forms such as kinetic energy, heat energy, radiant energy, chemical energy, potential energy.

• Energy is conserved. In an isolated system, the sum of all types of energy remains constant.

• Work is the energy added or removed from a body by a force acting over a distance.

• Power is the rate of expending energy.• Mass and energy are equivalent.

Some Kinds of Energy

• Kinetic Energy – the energy of moving objects• Heat, or thermal energy – of warm bodies.• Chemical Energy – of chemical reactions.• Gravitational Potential Energy – of a

gravitational field.• Electromagnetic Energy – energy associated

with electric and magnetic forces.• Mass Energy – all objects have energy by virtue

of their mass, the energy released in nuclear explosions.

Energy Units

Energy comes in many different forms and is measured in many different units. Some of the most common are:

Joules (J) = Newton-meter

*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.

Mass and Energy

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

E = mc2

where c is the speed of light. The speed of light is equal to c = 3108 meters/second.

Example: The energy of a NATS102 Student

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

E = mc2 = 80(3108)2 Joules E = 7.21018 Joules

convert to kilotons of TNTE = 7.21018 J x (1 kton/4.1841012 J) =1.7106 kilotons

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

Kinetic Energy

E = 1/2 mv2

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

Marion Jones Sprints to Victory in the 200 meter.

Kinetic Energy Examples1. A ball with mass of 0.01 kg traveling at 100 km/hour.

First convert v=100 km/hour to v=100,000 m/hour x 1hour/3600 sec=28 meters/secthen, E = 0.5 x 0.01 x (28)2 Joules

E = 3.9 Joules2. An asteroid, 10 km in diameter, with mass of 1x1013 kg traveling at

15 km/sec.First convert v=15 km/sec = 15,000 meters/sec

E = 0.5 x 1013 x (15,000)2 JoulesE = 1.1x1021 Joules

Convert to kilotons of TNTE = 1.1x1021 Joules x (1 kiloton/4.184x1012 Joules)E = 2.7x108 kilotons of TNT

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

Gravitational Potential Energy:

E = mgh

h = height

g = * 9.82 m/s2

m = mass

* On Earth

Example of Potential Energy

Cheryl Haworth lifts 297.6 lbsa distance of 2 meters

m = 297.6 lbs x 0.453 kg/lbs = 135 kg

mg = 135 kg x 9.8 m/s2 = 1.3103 Newtons E=mgh = 1.3103 N x 2 m= 2.6 103 Joules

E= 2.6 103 Joules (1 Cal/4186 J)

E = 0.63 Calories !!

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 Example

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

W = mah = 0.5 9.8 10 = 49 Joules

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

What’s going on???

Conservation of Energy

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

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

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

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

Conservation Laws in PhysicsConservation Laws in Physics

• Conservation laws are powerful tools used by physicists.

• Most fundamental quantities (mass, energy, & momentum) satisfy conservation laws.

• Conservation laws are easy – no vectors

Conservation of Energy

m = 50.9 kg

Work and Energy

Work = Force x distance

W = F x d

Joules = Newton x meters

Definition: Work is the energy added to an object through the action of forces over a distance.

PowerThe 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 Training

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

Lance Armstrong expends about 10,000 Calories in

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

Racing: Tour de France

Niagara Falls

570,000 kg of water descend every second.

The falls height is 55 meters.

Thus the potential energy of 1 kg of water is E=mha=19.855 J = 539 J.

The total power is thenP=570,000539 Joules/sec=3.1108 Wattsor 310 Megawatts.

Climbing out of the Grand Canyon

How big a lunch is needed?

Energy from lunch = Work to be done

W = mgh= (62 kg)(9.82m/s2)(1500 m)= 9.1x105 Joules

= 218 Calories

That is,

1 small peach & a glass of milk That’s it ??

Nope – we’re inefficient

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

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

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

Summary

Energy exists in many forms, for example in motion, the separationof masses, the separation of charges, mass…

We will work mainly with potential energy and kinetic energy in thisclass.

In a closed system, energy is conserved.

This principal allows us to predict motion with out dealing with vectors.

James Prescott Joule (1818-1889)Joule determined the mechanical equivalent of heat by measuring change in temperature produced by the friction of a paddlewheel attached to a falling weight in the 1840s. He made a series of measurements and found that, on average, a weight of 772 pounds falling through a distance of one foot would raise the temperature of one pound of water by 1° F. This corresponds to (772 ft lbs)(1.356 J/ft lb) = 59 453.6 Calories, or 1 cal = 4.15 Joules, in close agreement with the current accepted value of 1 calorie = 4.184 Joules.

The son of a prosperous brewer in North England, Joule financed his experiments himself.