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Section 1 Work, Power, and Machines. Chapter 12. Math Skills. Work Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N?. Given: force, F = 190 N - PowerPoint PPT PresentationTRANSCRIPT
Section 1 Work, Power, and Machines
Math Skills
Work Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N?
Chapter 12
Given: force, F = 190 Ndistance, d = 2.0 m
Unknown: work, W = ? J
Section 1 Work, Power, and Machines
Math Skills, continued
2. Write the equation for work.
Chapter 12
work = force distanceW = f d
3. Insert the known values into the equation, and solve.
W = 190 N 2.0 m = 380 N•mW = 380 J
Section 1 Work, Power, and Machines
Math Skills
Power It takes 100 kJ of work to lift an elevator 18 m. If this is done in 20 s, what is the average power of the elevator during the process?
Chapter 12
Given: work, W = 100 kJ = 1 105 Jtime, t = 20 s
The distance of 18 m will not be needed to calculate power.
Unknown: power, P = ? W
Section 1 Work, Power, and Machines
Math Skills, continued
3. Insert the known values into the equation, and solve.
2. Write the equation for power.
power work
time
P W
t
P 1 105 J
20 s 5 103 J/s
P 5 103 W 5 kW
Chapter 12
Section 1 Work, Power, and Machines
Math Skills Mechanical Advantage Calculate the mechanical
advantage of a ramp that is 5.0 m long and 1.5 m high.
.
Chapter 12
Given: length= 5.0 mheight= 1.5 m
Unknown: mechanical advantage = ?
Section 1 Work, Power, and Machines
Math Skills, continued
2. Write the equation for mechanical advantage.
mechanical advantage
input distance
output distance
3. Insert the known values into the equation, and solve.
mechanical advantage
5.0 m
1.5 m 3.3
Chapter 12
Math Skills
Gravitational Potential Energy A 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff?
1. List the given and unknown values.Given: mass, m = 65 kg
height, h = 35 mfree-fall acceleration, g = 9.8 m/s2
Unknown: gravitational potential energy, PE = ? J
Section 3 What is Energy?Chapter 12
Math Skills, continued
2. Write the equation for gravitational potential energy.
Section 3 What is Energy?Chapter 12
PE = mgh
3. Insert the known values into the equation, and solve.
PE = (65 kg)(9.8 m/s2)(35 m)PE = 2.2 104 kg•m2/s2
PE = 2.2 104 J
Math Skills
Kinetic Energy What is the kinetic energy of a 44 kg cheetah running at 31 m/s?
1. List the given and unknown values.Given: mass, m = 44 kg
speed, v = 31 m/s
Unknown: kinetic energy, KE = ? J
Section 3 What is Energy?Chapter 12
Math Skills, continued
2. Write the equation for kinetic energy.
kinetic energy 1
2 mass speed squared
KE 1
2mv 2
3. Insert the known values into the equation, and solve.
KE 1
2(44 kg)(31 m/s)2
KE 2.1 104 kggm2 /s2
KE 2.1 104 J
Section 3 What is Energy?Chapter 12
Section 4 Conservation of Energy
Math Skills
Efficiency A sailor uses a rope and an old, squeaky pulley to raise a sail that weighs 140 N. He finds that he must do 180 J of work on the rope in order to raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the pulley? Express your answer as a percentage.
1. List the given and unknown values.Given: work input = 180 J
useful work output = 140 J
Unknown: efficiency = ? %
Chapter 12
Section 4 Conservation of Energy
Math Skills, continued
2. Write the equation for efficiency.
efficiency
useful work output
work input
3. Insert the known values into the equation, and solve.
140 J0.78
180 JTo express this as a percentage, multiply by 100
and add the percent sign, "%."
0.78 100% 78%
efficie
effici
ncy
ency
Chapter 12
Concept MapSection 4 Conservation of Energy
Chapter 12
Understanding Concepts, continued3. Which of these statements describes the law
of conservation of energy?
A. No machine is 100% efficient.B. Energy is neither created nor destroyed.C. The energy resources of Earth are limited.D. The energy of a system is always decreasing.
Standardized Test PrepChapter 12
Understanding Concepts, continued3. Which of these statements describes the law
of conservation of energy?
A. No machine is 100% efficient.B. Energy is neither created nor destroyed.C. The energy resources of Earth are limited.D. The energy of a system is always decreasing.
Standardized Test PrepChapter 12
4. A coal-burning power plant produces electrical energy with an efficiency of 30%. If the chemical energy produced by burning one gram of coal is 25,000 joules (J), how many joules of electrical energy are produced by the combustion of one gram of coal?
Standardized Test PrepChapter 12
Understanding Concepts, continued4. A coal-burning power plant produces
electrical energy with an efficiency of 30%. If the chemical energy produced by burning one gram of coal is 25,000 joules (J), how many joules of electrical energy are produced by the combustion of one gram of coal?
Answer: 7500 J
Standardized Test PrepChapter 12
Interpreting Graphics6. If the input force on
this pulley system is 100 N, what is the output force?
F. 100 NG. 200 NH. 300 NI. 400 N
Standardized Test PrepChapter 12
Interpreting Graphics, continued
6. If the input force on this pulley system is 100 N, what is the output force?
F. 100 NG. 200 NH. 300 NI. 400 N
Standardized Test PrepChapter 12
Interpreting Graphics, continued
Standardized Test PrepChapter 12
7. How could the amount of force required to raise the bucket be decreased even more?A. Add additional pulleys.B. Increase the length of the rope.C. Thread the rope through the pulleys in opposite order.D. Increase the amount
of force on the free end of the rope.
Interpreting Graphics, continued7. How could the amount of
force required to raise the bucket be decreased even more?A. Add additional pulleys.B. Increase the length of the rope.C. Thread the rope through the pulleys in opposite order.D. Increase the amount
of force on the free end of the rope.
Standardized Test PrepChapter 12
Practice Problems#8. A crane lifts an 8,000 N beam 75 m to the top of a
building in 30 seconds. How much power does the crane use?
W
F D
Power = Work Time
Work Triangle
Work = Force X Distance
Work = 8,000 N X 75 m
Work = 600,000 J
Power = 600,000 J 30 s
Power = 20,000 W
P
W
T
Power Triangle
Practice Problems#9. A motor exerts a force of 10,000 N to lift an elevator
6 m in 5 seconds. What is the power produced by the motor?
W
F D
Power = Work Time
Work Triangle
Work = Force X Distance
Work = 10,000 N X 6 m
Work = 60,000 J
Power = 60,000 J 5 s
Power = 12,000 W
P
W
T
Power Triangle
Practice Problems#10. A tow truck exerts a force of 9,000 N to pull a car
out of a ditch. It moves the car a distance of 6 m in 25 s. What is the power of the tow truck?
W
F D
Power = Work Time
Work Triangle
Work = Force X Distance
Work = 9,000 N X 6 m
Work = 54,000 J
Power = 54,000 J 25 s
Power = 2,160 W
P
W
T
Power Triangle
Identify one form of potential energy and one form of kinetic energy.
Practice Problems12. An 80 kg man is jogging at a velocity of
4 m/s. What is his kinetic energy?
K.E. = mv2
2
K.E. = 80 kg X (4 m/s)2
2K.E. = 80 kg X 16 m/s 2
K.E. = 640 J