Transcript Work & Energy

Work
&
Energy
Introductory Physics – Kinematics and Mechanics
Distance and displacement
Speed and Velocity
Acceleration
Kinematic formulas
Forces – Contact and Non-contact
Newton’s laws of motion
Gravity and Friction
Forces Do Work
x
Here, the force is exerted on the car to get it to move from
rest. In physics, we say that the force F did work on the car.
Kinetic Frictional Force Does Work
x
Here, the frictional force was exerted on the sled to slow it to
a stop. In physics, we say that the frictional force did work on
the sled.
Work Done by a Constant Force
Definition: Work Done by a Constant Force
The work done on an object by a constant force F is
W  ( F cos  ) x
cos 0  1
where F is the magnitude of the force, x is the
magnitude of the displacement, and  is the angle cos 90  0
between the force and the displacement.
cos 180  1
The SI Unit for work is newton · meter = joule (J).
Accelerating a Crate
The truck is accelerating at
a rate of +1.50 m/s2. The mass
of the crate is 120-kg and it
does not slip. The magnitude of
the displacement is 65 m.
What is the total work done on
the crate by all of the forces
acting on it?
The angle between the
displacement and the normal
force is 90 degrees.
The angle between the
displacement and the weight is
also 90 degrees.
W   F cos90  x  0
fs  ma
 120 kg 1.5m s
2

 180N
The angle between the displacement
and the friction force is 0 degrees.
W   fs cos0  x
 180N cos0   65 m 
 1.2  10 4 J
x
x
Find the work done if the force is 45.0-N, the angle is 50.0
degrees, and the displacement is 75.0 m.
W   F cos   x
  45.0 N cos50.0   75.0 m 
 2170 J
If you do some work, you expect to
get something for it.
In physics, when a net force does
some work on an object, the result is
a change in the kinetic energy of the
object.
Kinetic Energy
Definition: Kinetic Energy
The kinetic energy of an object with mass m and
speed v is
KE  mv
1
2
2
The SI Unit for Kinetic Energy is joule (J).
Work – Energy Theorem
When a net external force does work W on an object, the
kinetic energy of the object changes from its initial value of
KE0 to a final value KEF, the difference between the two
values is equal to the work:
W  KEF  KE0
 mv  mv
1
2
2
F
1
2
2
0
x
Find the distance x the sled slides, if the magnitude of
the kinetic frictional force is 35 N and the combined mass
of the sled and rider is 70.0 kg.
Using Energy - Example
Accelerating a Car
A car is waiting for a traffic light to change. How much
energy do you need to accelerate the 1500-kg car from 0
to 22 m/s?
Gasoline Used?
W  KE  12 mvF2  12 mv02 Each liter of gas has
an energy equivalent
 12 (1500 kg)(22 m/s) 2 of 3.3  107 J.
 3.6 105 J
 1 liter
V  3.6 10 J
7
3
.
3

10

 0.01 liter
5


J
Using Energy
Accelerating a Car
A certain amount of energy is used to accelerate a car
from 0 m/s to a speed v. How much more energy is
required to accelerate from v to 2v?
Gravitational Potential Energy
•
The work done by the force of gravity on an object is:
W  (mg cos )(h0  hF )
•
This is equal to the gravitational potential energy PE that
an object has by virtue of its position relative to the
surface of the earth.
•
That position is measured by the height h of the object
relative to an arbitrary zero level.
PE = mgh
A dam blocks the passage of a
river and generates electricity.
Approximately, 57 000 kg of
water fall each second through
a height of 19 m. How much
potential energy is converted to
kinetic energy each second?
Conservation of Mechanical Energy
Principle of Conservation of Mechanical Energy
The total mechanical energy
E = KE + PE
of an object remains constant as the object moves, provided
that the net work done by non-conservative forces is zero.
Conservative Forces
Non-Conservative Forces
Gravitational Force
Elastic Spring Force
Electric Force
Friction
Normal Force
Propulsion Force of a
Rocket or a Motor
Conservation of Mechanical Energy
Conservation of Mechanical Energy - Example
Daredevil Jumping
A motorcyclist
attempts to leap a
canyon by driving
horizontally off a
cliff.
When it leaves the cliff, the cycle has a speed of 38.0 m/s.
Ignoring air resistance, find the speed with which the cycle
hits the ground on the other side.
Conservation of Mechanical Energy - Example
WNC  0 J
EF



 
E0 

2
2
1
1
mv

mgh

mv
F
F
0  mgh0
2
2
A quarter is dropped from rest from the fifth floor of a
very tall building. The speed of the quarter is v just
before striking the ground. From what floor would the
quarter have to be dropped from rest for the speed just
before striking the ground to be approximately 2v?
Ignore all air resistance effects to determine your
answer.
For fall from 5th story…
E0
EF
1
2
mv  mghf  mv  mgh0
1
2
mv f2  mgh0
2
f
v f  2gh0
1
2
2
0
For 2vf multiply both side by 2 and find the new initial height.
2v f  2 2gh0  (4)2gh0  2g (4h0 )
Comparing, this with the first case,
you can see that the height is 4 times the initial height.
Principle of Conservation of Energy
Energy can neither be created nor
destroyed, but can only be converted
from one form to another.
Forms of Energy:
Chemical – Nuclear – Radiant – Thermal –
Sound – Electrical - Mechanical
Each liter of gas has
an energy equivalent
of 3.3  107 J.
This is equivalent to…
one Burger King value
meal is 5 441 800 J.
So, 6 such meals equals
one liter of gasoline.
one
of coal
a 100kilogram
W computer
monitor on for 90
hours
Food Calories
Usually, the energy content of food is expressed in
Calories. The energy stored in food is a form of
chemical energy that is released as we digest it.
One Calorie = 1000 calories = 4186 J.
•
•
•
•
•
•
•
1 cup of lettuce = 10 Calories = 42 000 J
1 cup of carrots = 45 Calories = 188 000 J
12 ounce light beer = 95 Calories = 398 000 J
plain baked potato = 145 Calories = 607 000 J
piece of apple pie = 405 Calories = 1.7 million J
1 cup of rice = 670 Calories = 2.8 million J
double cheeseburger = 1050 Calories = 4.4 million J
Food Calories
Suppose a 65-kg hiker eats a 250 C snack. So the
snack contains…
If this were all (100 %) converted into potential energy
mg(hF  h0), we can find the equivalent change in height.
PE  mg (hf  h0 )
PE
1.0 106 J
hF  h0 

 1600 m
2
mg (65 kg)(9.80 m/s )
Efficiency
• Not all of the energy is converted to usable work,
some goes to other things such as producing an
increase in body temperature.
• A more realistic estimate would be that 25% of
the food calories would be used up in climbing, the
rest goes to other things.
• The net result of all of this is that the climber
could only climb a quarter of the way, about 400 m
on that 250-Calorie snack.
Similarly, in a moving car the chemical energy of
the gasoline is converted into kinetic energy,
electrical energy, and heat.
Power
Average Power
Average power Pave is the average rate of
work W is done; and it’s obtained by
dividing W by the time required to
perform the work:
work W
Pave 

time
t
The SI unit for power is: joule/s = watt (W)
Power
A dam blocks the passage of a river and generates electricity.
Approximately, 57 000 kg of water fall each second through a height
of 19 m. If one half of the gravitational potential energy of the water
were converted to electrical energy, how much power would be
generated?
P = E / t = ½ mgh / t = ½ (57 000 kg)(9.8 m/s2)(19 m) / (1 s)
= 5.3 x 106 J / s = 5300 kW
kilowatt - hour
One kilowatt-hour is the amount of work or energy
generated when one kilowatt of power is supplied for a
time of one hour.
Power
A television is rated at 150 watts. (a) What is the cost of
operating the TV for 5 hours if the utility charges $0.11
per kilowatt-hour? (b) How many joules of energy are
purchased?
(a)
E = Pt = (150 W)(5 h) = 750 W-h = 0.75 kW-h
Cost = (0.75 kW-h)($0.11/kW-h) = $0.08
(b) 0.75 kW-h  1000 W  1 J/s  3600 s   2.7  106 J
 1 kW  1 W  1 h 




Power
Clock radio = 10 W
Hair dryer = 1200 – 1875 W
Coffee maker = 900 – 1200 W
Microwave oven = 750 – 1100 W
Clothes washer = 350 – 500 W
Laptop = 50 – 100 W
Clothes dryer = 1800 – 5000 W
Dishwasher = 1200 – 2400 W (using the drying feature greatly increases energy
consumption)
Fans
Heater (portable) = 750 – 1500
Ceiling = 65–175 W
Clothes iron = 1000 - 1800 W
Window = 55–250 W
Toaster = 800 – 1400 W
Furnace = 750 W
VCR/DVD = 17–21 / 20–25 W
Whole house = 240 – 750
Refrigerator (frost-free, 16 cubic feet) = 725 W
Televisions (color)
Water heater = 4500 – 5500 W
19" = 65 – 110 W
27" = 113 W
36" = 133 W
53“ - 61" Projection = 170 W
Flat screen = 120 W