Download Chapter 6 Work, Energy, and Power

Chapter 6
Work, Energy, and Power
Copyright © 2010 Pearson Education, Inc.
What Is Physics All About?
•  Matter
•  Energy
•  Force
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Work Done by a Constant Force
The definition of work, when the force is
parallel to the displacement:
W = Fs
SI unit: newton-meter (N·m) = joule, J
s
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Work Done by a Constant Force
If the force is at an angle to the displacement:
W = (F cos θ)s
s
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Sally pulls a car with a rope. Exerting a force of
150N, she accelerates the car from rest to a speed of
25.0 km/hr in 300m. The angle of the rope is 15.00.
The force of kinetic friction is 90.0N. What is the
mass of the car? What is the work done by Sally?
Fy
F = 150N
θ = 15°
Fx
s = 300m
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•  Solution
vi = 0m/s
vf = 6.944m/s
s = 300m
θ  = 15.00
F = 150N
Ff = 90.0N
vf2 = vi2 + 2as
6.9442 = 0 + 2a(300)
a = 0.0804 m/s
Fnet = ma
Fx – Ff = ma
150cos15.0° – 90.0 = m(0.0804)
m = 683 kg
WSally = (Fx + Ff)s
WSally = (150cos15° + 90.0)(300)
WSally = 7.05 X 104 J
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Work Done by a Constant Force
The work done may be positive, zero, or
negative, depending on the angle between the
force and the displacement:
s
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s
s
Positive work
accelerates an
object
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Negative work
decelerates an
object
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Kinetic Energy
By definition, KE = ½mv2
The units of KE are the same
as the units of work: joules
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How is Energy Related to Work?
W = Fs
F = ma
W = mas
vf2 = vi2 + 2as
vf2 – vi2 = 2as
½(vf2 – vi2) = as
W = m ½(vf2 – vi2)
W = ½mvf2 – ½mvi2
Work-Kinetic Energy Theorem: The work done on
an object is equal to its change in kinetic energy.
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Power
Power is a measure of the rate at which work is
done:
SI unit: J/s = watt
1 horsepower = 1 hp = 746 watts
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Power
If an object is moving at a constant speed
against friction, gravity, and air resistance, the
power exerted by the driving force can be
written:
s
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s
•  Problem
– Jon pulls a sled along a snowy path using
a rope that makes a 45.0° angle with the
ground. Jon pulls with a force of 42.3N.
The sled moves at 5.33 m/s. Assuming no
friction, what power does Jon produce?
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•  Solution
F = 42.3N
v = 5.33s
θ = 45.00
Fs
P=
= F cosθ v = (42.3)(cos 45.0°)(5.33) = 159w
t
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Potential Energy
Kinetic energy (KE) is the energy of motion;
potential energy (PE) is stored energy.
A pine cone about to fall from a certain height has
PE. As it falls, the PE is released as KE.
A spring that is stretched to a certain distance has
PE. As it unstretches, the PE is released as KE.
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Gravitational Potential Energy
If we pick up a ball from one shelf and put it on a
higher shelf, we have done work on the ball. There is
no change in kinetic energy, but there is a change in
potential energy, or PE. Like KE, it is measured in
joules.
PEG = mgh
W = mg(hf – hi)
hf – hi
W = mghf – mghi
= PEGf – PEGi
hf
hi
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Work-Energy Theorem: The total work done on an
object is equal to its change in kinetic energy
plus its change in potential energy plus any work
done to overcome friction.
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Conservation of Mechanical Energy
Definition of mechanical energy:
Em = KE + PEG
The mechanical energy of a system is conserved.
KEf + PEGf = KEi + PEGi
“Energy Skate Park”
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Conservation of Mechanical Energy
Energy conservation can be used to solve many
problems involving velocity and acceleration.
Example: If I drop a 20.0 kg mass from a height
of 50.0 meters, at what speed will it hit the ground?
KEf + PEGf = KEi + PEGi
KEf + 0 = 0 + PEGi
½mvf2 = mghi
½vf2 = ghi
½vf2 = (9.81)(50.0)
v = 31.3 m/s
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Conservation of Mechanical Energy
Example: If I shoot a 10.0 g bullet straight up into
the air from a height of 2.30 meters with a velocity
of 200 m/s, how high will it go?
KEf + PEGf = KEi + PEGi
0 + mghf = ½mvi2 + mghi
(0.01)(9.81)hf = ½(0.01)(200)2 + (0.01)(9.81)(2.30)
hf = 2.04 km
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Homework
pp. 203-207 23, 31, 49, 61, 75, 93, 95
Chapter 5 Review:
pp. 167-169 9, 23, 41, 62 (avg. distance from
earth to sun is 149,597,890 km, vt of earth is
107,300 km/h, mass of earth is 5.98 X 1024 kg)
Chapter 4 Review:
pp. 131-138 33, 41, 128
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