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Work, Power, and Machines
What is Work?
transfer of energy to a body by application of a force that causes body to move in direction of force.
W = F d
What is Work?
SI units: joules (J).• 1 J = 1 N•m = 1 kg•m2/s2
Chapter 12
WORKImagine 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:
W = ?
F = 190 N
d = 2.0 m
WORK:
W = Fd
W = (190 N) (2.0 m)
W = 380 J
FW
d
WORKA crane uses an average force of 5200 N to lift a girder 25 m. How much work does the crane do on the girder?
GIVEN:
W = ?
F = 5200 N
d = 25 m
WORK:
W = Fd
W = (5200 N) (25 m)
W = 130,000 J or
1. 3 x 105 JFW
d
WORKAn apple weighing 1 N falls through a distance of 1 m. How much work is done on the apple by the force of gravity?
GIVEN:
W = ?
F = 1 N
d = 1m
WORK:
W = Fd
W = (1 N) (1 m)
W = 1 J
FW
d
Power
rate at which work is done or energy is transformed.
SI Unit: watts.• watt (W) = 1 J/s
Power = work
time
Chapter 12
p= W/t
POWERIt 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?
GIVEN:
p = ?
W = 1 x 105 J
t = 20 s
WORK:
p = W/t
p = 1 x 105 J / 20 s
p = 5 x 103 W or 5 kW
pW
t
POWERWhile rowing across the lake during a race, John does 3960 J of work on the oars in 60.0 s. What is his power output in watts?
GIVEN:
p = ?
W = 3960 J
t = 60 s
WORK:
p = W/t
p = 3960 J / 60 s
p = 66.0 W
pW
t
POWERUsing a jack, a mechanic does 5350 J of work to lift a car 0.500 m in 50.0 s. What is the mechanic’s power output?
GIVEN:
p = ?
W = 5350 J
t = 50 s
WORK:
p = W/t
p = 5350 J / 50 s
p = 107 W
pW
t
Machines
Machines multiply and redirect forces.• help people by redistributing work put into
them.• change either size or direction of input force.
allows same amount of work to be done by either decreasing distance while increasing force or by decreasing force while increasing distance.
Force and Work
Chapter 12
Mechanical Advantage
tells how much a machine multiplies force or increases distance.
mechanical advantage = output force = input distance input force output distance
ma
id
od ma
of
if
MECHANICAL ADVANTAGECalculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high.
GIVEN:
ma = ?
id = 5.0 m
od = 1.5 m
WORK:
ma = id/od
ma = 5.0 m / 1.5 m
ma = 3.3
ma
id
od
MECHANICAL ADVANTAGECalculate the mechanical advantage of a ramp that is 6.0 m long and 1.5 m high.
GIVEN:
ma = ?
id = 6.0 m
od = 1.5 m
WORK:
ma = id/od
ma = 6.0 m / 1.5 m
ma = 4
ma
id
od
MECHANICAL ADVANTAGEDetermine the mechanical advantage of an automobile jack that lifts a 9900 N car with an input force of 150 N.
GIVEN:
ma = ?
of = 9900 N
if = 150 N
WORK:
ma = of/if
ma = 9900 N / 150 N
ma = 66
ma
of
if
SIMPLE MACHINES
The Lever Family
simple machines One of six basic types of machines which are basis for
all other forms of machines. have a rigid arm and a fulcrum.
six types divided into two families.lever family: inclined plane family:
simple lever
(3 types)
simple inclined plane
pulley wedge
wheel and axle screw
First Class Levers
fulcrum located between points of application of input and output forces.
Second Class Levers
• fulcrum is at one end of arm and input force is applied to other end.
Third Class Levers
• multiply distance rather than force. • have a mechanical advantage of less than 1.
Pulleys
are modified levers.• point in middle of a
pulley is like fulcrum of a lever.
• single, fixed pulley has a m. a. of 1.
• block and tackle: Multiple pulleys working together
Wheel & Axle
a lever or pulley connected to a shaft.• steering wheel of a car, screwdrivers, and cranks
The Inclined Plane Family
multiply and redirect force.• turns small input force into large output
force by spreading work out over a large distance.
Simple Inclined Plane
Changes both magnitude & direction of force
Wedge
Functions as two inclined planes back to back.
Turns single downward force into two forces directed out to sides.
Screw
an inclined plane wrapped around a cylinder.
Compound Machines
machine made of more than one simple machine
Examples :scissors
• two first class levers joined at a common fulcrum
car jack • combination of lever
with a large screw
Chapter 12
What is Energy?
Energy
Energy: ability to do work.• When you do work on an object, you transfer
energy to that object.• Whenever work is done, energy is transformed
or transferred to another system. SI Units: joules (J)
Chapter 12
Potential Energy
energy that an object has because of position, shape, or condition
stored energy.
Elastic potential energy:• energy stored in any type of stretched or
compressed elastic material, (spring or a rubber band).
Gravitational potential energy• energy stored in gravitational field which exists
between any two or more objects.
Gravitational Potential Energy
depends on both mass and height.
PE = mgh
The height can be relative.• height used in above equation is usually
measured from ground. • However, it can be a relative height between two
points, such as between two branches in a tree.
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?
GIVEN:
m = 65 kg
h = 35 m
g= 9.8 m/s2
PE = ?
WORK:
PE = mgh
PE = (65 kg) (35 m) (9.8 m/s2)
PE = 2.2 x 104 kg•m2/s2
2.2 x 104 J
Kinetic Energy
energy of a moving object due to object’s motion depends on mass and speed. depends on speed more than mass.
kinetic energy 1
2mass speed squared
KE 1
2mv 2
KINETIC ENERGY
What is the kinetic energy of a 44 kg cheetah running at 31 m/s?
GIVEN:
KE = ?
m = 44 kg
v= 31 m/s
WORK:
KE = ½ mv2
KE = ½ (44 kg) (31 m/s)2
KE = 2.1 x 104 kg x m2/s2 or 2.1 x104 J
KINETIC ENERGY
Calculate the kinetic energy in joules of a 1500 kg car moving at 29 m/s.
GIVEN:
KE = ?
m = 1500 kg
v= 29 m/s
WORK:
KE = ½ mv2
KE = ½ (1500 kg) (29 m/s)2
KE = 6.3 x105 J
KINETIC ENERGY
Calculate the kinetic energy in joules of a 1500 kg car moving at 18 m/s.
GIVEN:
KE = ?
m = 1500 kg
v= 18 m/s
WORK:
KE = ½ mv2
KE = ½ (1500 kg) (18 m/s)2
KE = 2.4 x105 J
Other Forms of Energy
mechanical energy: amount of work an object can do because
of object’s kinetic & potential energies you can SEE it Large scale basis
nonmechanical energy. you CANNOT SEE it X rays, microwaves Small scale basis (atomic)
Other Forms of Energy
Atoms and molecules• kinetic energy of particles related to heat and
temperature.
Chemical reactions Breaking bonds exothermic/endothermic
Photosynthesis turn energy in sunlight into chemical energy.
Chapter 12
Other Forms of Energy
nuclear fusion reactions Combining of atomic nuclei
Electricity.• derived from flow of charged particles• bolt of lightning or in a wire.
electromagnetic waves.• Light energy from sun
CONSERVATION OF ENERGY
Energy Transformations
readily changes from one form to another.
Potential energy changes into kinetic energy.• car goes down a hill on a roller coaster, potential
energy changes to kinetic energy.
Kinetic energy changes into potential energy.• kinetic energy a car has at bottom of a hill can do
work to carry car up another hill.
Energy Transformations
Mechanical energy can change to nonmechanical energy as a result of friction, air resistance, or other means.
The Law of Conservation of Energy
energy cannot be created or destroyed. doesn’t disappear, it changes to another
form.
if total energy in a system increases, it must be due to energy that enters the system from an external source.
SYSTEMS
closed system • when flow of energy into and out of a system
is small enough that it can be ignored
open systems (most)• exchange energy with the space that
surrounds them.
Efficiency of Machines
Not all of the work done by a machine is useful work.• cannot do more work than work required to
operate machine.• Because of friction, work output of a machine is
always somewhat less than work input.
Efficiency: ratio of useful work out to work in. measure of how much useful work it can do.• expressed as a percentage.
Efficiency of Machines
Efficiency Equation
Machines need energy input.• Because energy always leaks out of a
system, every machine needs at least a small amount of energy input to keep going.
efficiency
useful work output
work input
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.
GIVEN:
eff = ?
uwo = 140 J
wi= 180 J
WORK:
eff = uwo/wi
eff = 140 J / 180 J
eff = 0.78 or 78 %
eff
uwo
wi
EFFICIENCY Alice & Jim calculate that they must do 1800 J of work to push a piano up a ramp. However, because they must also overcome friction, they must actually do 2400 J of work. What is the efficiency of the ramp?
GIVEN:
eff = ?
uwo = 1800 J
wi= 2400 J
WORK:
eff = uwo/wi
eff = 1800 J / 2400 J
eff = 0.75 or 75 %
eff
uwo
wi
EFFICIENCY It takes 1200 J of work to lift the car high enough to change a tire. How much work must be done by the person operating the jack if the jack is 25% efficient
GIVEN:
eff = 25%
uwo = 1200 J
wi= ?
WORK:
wi = uwo/eff
wi = 1200 J / .25
wi = 4800 J
eff
uwo
wi