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Copyright © 2010 Pearson Education, Inc.
Chapter 6 Work, Energy, and Power
Copyright © 2010 Pearson Education, Inc.
What Is Physics All About? • Matter • Energy • Force
Copyright © 2010 Pearson Education, Inc.
Work Done by a Constant Force The definition of work, when the force is parallel to the displacement:
SI unit: newton-meter (N·m) = joule, J
W = Fs
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?
F = 150N
θ = 15°
Fy
Fx
s = 300m
Copyright © 2010 Pearson Education, Inc.
• Solution vi = 0m/s vf = 6.944m/s s = 300m θ = 15.00 F = 150N Ff = 90.0N
Fnet = ma
vf2 = vi
2 + 2as 6.9442 = 0 + 2a(300)
a = 0.0804 m/s
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
Fx – Ff = ma
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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 s s
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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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F = ma W = Fs
vf2 = vi
2 + 2as W = mas
vf2 – vi
2 = 2as ½(vf
2 – vi2) = as W = m ½(vf
2 – vi2)
W = ½mvf2 – ½mvi
2
How is Energy Related to Work?
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 s
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• 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?
Copyright © 2010 Pearson Education, Inc.
• Solution F = 42.3N v = 5.33s θ = 45.00
P = Fst= F cosθv = (42.3)(cos45.0°)(5.33) =159w
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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.
Copyright © 2010 Pearson Education, Inc.
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 = mghf – mghi hf
hf – hi
hi
= PEGf – PEGi
W = mg(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 ½mvf
2 = 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 = ½mvi
2 + 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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