Work

1
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 natures way of making certain that
  everything doesn't happen all at once.
• -Woody Allen

2
Forces are vectors
y
Fma means Fx(total) max
Fy(total) may or F(total) ma
F
Fy
x
Fx
You can consider perpendicular motion
independently.
3
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.

4
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.

5
Energy Units

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

Calories with a small c, cal Cal/1000.
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
Mass and Energy

• One of Einsteins 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 3?108 meters/second.

11
Example The energy of a NATS102 Student

• A NATS102 student has a mass of 80 kg (170 lbs).
  According to Einsteins equation, he/she has an
  energy of
• E mc2 80?(3?108)2 Joules
• E 7.2?1018 Joules
• convert to kilotons of TNT
• E 7.2?1018 J x (1 kton/4.184?1012 J) 1.7?106
  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.

12
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.
13
Kinetic Energy Examples

• 1. A ball with mass of 0.01 kg traveling at 100
  km/hour.
• First convert v100 km/hour to v100,000
  m/hour x 1hour/3600 sec28 meters/sec
• then, E 0.5 x 0.01 x (28)2 Joules
• E 3.9 Joules
• 2. An asteroid, 10 km in diameter, with mass of
  1x1013 kg traveling at 15 km/sec.
• First convert v15 km/sec 15,000 meters/sec
• E 0.5 x 1013 x (15,000)2 Joules
• E 1.1x1021 Joules
• Convert to kilotons of TNT
• E 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

14
Gravitational Potential Energy
E mgh h height g 9.82 m/s2 m mass
On Earth
15
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 1.3?103 Newtons Emgh
1.3?103 N x 2 m 2.6 ?103 Joules E 2.6 ?103
Joules ? (1 Cal/4186 J) E 0.63 Calories !!
16
Another Kinetic Energy Example

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
17
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.
• Whats going on???

18
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, )

19
Conservation 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

20
Conservation of Energy
m 50.9 kg
21
Work and Energy
Definition Work is the energy added to an object
through the action of forces over a distance.
22
(No Transcript)
23
Power
The 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
24
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.

Racing Tour de France
Lance training in Arizona
25
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
  Emha1?9.8?55 J 539 J.
• The total power is thenP570,000?539
  Joules/sec3.1?108 Wattsor 310 Megawatts.

26
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 Thats it ??

27
Nope were 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.

28
Summary
Energy exists in many forms, for example in
motion, the separation of masses, the separation
of charges, mass We will work mainly with
potential energy and kinetic energy in
this class. In a closed system, energy is
conserved. This principal allows us to predict
motion with out dealing with vectors.
29
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.