Transcript Chap 12 Math review

Chapter 12
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?
Given:
Unknown:
force, F = 190 N
distance, d = 2.0 m
work, W = ? J
Chapter 12
Section 1 Work, Power, and Machines
Math Skills, continued
2. Write the equation for work.
work = force  distance
W=f d
3. Insert the known values into the equation, and solve.
W = 190 N  2.0 m = 380 N•m
W = 380 J
Chapter 12
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?
5
work, W = 100 kJ = 1  10 J
time, t = 20 s
The distance of 18 m will not be needed to
calculate power.
Unknown: power, P = ? W
Given:
Chapter 12
Section 1 Work, Power, and Machines
Math Skills, continued
2. Write the equation for power.
work
power 
time
W
P
t
3. Insert the known values into the equation,
and solve.
5
1 10 J
P
 5  103 J/s
20 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.
. Given:
length= 5.0 m
Unknown:
height= 1.5 m
mechanical advantage = ?
Chapter 12
Section 1 Work, Power, and Machines
Math Skills, continued
2. Write the equation for mechanical
advantage.
input distance
mechanical advantage 
output distance
3. Insert the known values into the equation, and solve.
mechanical advantage 
5.0 m
 3.3
1.5 m
Chapter 12
Section 3 What is Energy?
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 m
free-fall acceleration, g = 9.8 m/s2
Unknown: gravitational potential energy, PE = ? J
Chapter 12
Section 3 What is Energy?
Math Skills, continued
2. Write the equation for gravitational potential
energy.
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
Chapter 12
Section 3 What is Energy?
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
Chapter 12
Section 3 What is Energy?
Math Skills, continued
2. Write the equation for kinetic energy.
1
kinetic energy   mass  speed squared
2
1
KE  mv 2
2
3. Insert the known values into the equation, and solve.
1
KE  (44 kg)(31 m/s)2
2
KE  2.1 10 4 kggm2 /s2
KE  2.1 10 4 J
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.
useful work output
efficiency 
work input
3. Insert the known values into the equation, and solve.
140 J
efficiency 
 0.78
180 J
To express this as a percentage, multiply by 100
and add the percent sign, "%."
efficiency  0.78  100%  78%
Chapter 12
Section 4 Conservation of Energy
Concept Map
Chapter 12
Standardized Test Prep
Understanding Concepts, continued
3. 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.
Chapter 12
Standardized Test Prep
Understanding Concepts, continued
3. 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.
Chapter 12
Standardized Test Prep
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?
Chapter 12
Standardized Test Prep
Understanding Concepts, continued
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?
Answer: 7500 J
Chapter 12
Standardized Test Prep
Interpreting Graphics
6. If the input force on
this pulley system is
100 N, what is the
output force?
F.
G.
H.
I.
100 N
200 N
300 N
400 N
Chapter 12
Standardized Test Prep
Interpreting Graphics,
continued
6. If the input force on
this pulley system is
100 N, what is the
output force?
F.
G.
H.
I.
100 N
200 N
300 N
400 N
Chapter 12
Standardized Test Prep
Interpreting Graphics,
continued 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.
Chapter 12
Standardized Test Prep
Interpreting Graphics,
continued 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.
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?
Power = Work
Time
Work = Force X Distance
Work = 8,000 N X 75 m
Power = 600,000 J
30 s
Work = 600,000 J
Power = 20,000 W
W
F
W
D
P
Work Triangle
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?
Power = Work
Time
Work = Force X Distance
Work = 10,000 N X 6 m
Power = 60,000 J
5s
Work = 60,000 J
Power = 12,000 W
W
F
W
D
P
Work Triangle
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?
Power = Work
Time
Work = Force X Distance
Work = 9,000 N X 6 m
Power = 54,000 J
25 s
Work = 54,000 J
Power = 2,160 W
W
F
W
D
P
Work Triangle
T
Power Triangle
Identify one form of potential energy and one form of kinetic energy.
Practice Problems
12. 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
2
K.E. = 80 kg X 16 m/s
2
K.E. = 640 J