Transcript Kinetic Energy

Energy
Chapter 9
Objectives
Define and describe work.
 Define and describe power.
 State the 2 forms of mechanical energy.
 State 3 forms of potential energy.
 Describe how work and kinetic energy are
related.
 State the work-energy theorem.
 State the law of conservation of energy.
 Describe how a machine uses energy.
 Explain why no machine can have an
efficiency of 100%.
 Describe the role of energy in living
organisms.

9.1 Work
 Recall
that a change in an object’s
momentum is related to an impulse
–a force and how long the force acts.
 “How long” does not always mean
time, however. It can also mean
distance.
 Force x distance = work
Work is the product of the force on an
object and the distance through which
the object is moved.
9.1 Work
 For
work to be done in Physics,
a force acts on an object and the
object moves in the direction of
the force.
Work is done on a load when you
lift it against Earth’s gravity.
No work is done on the load to
hold it once it has been lifted or to
carry the load around the room.
9.1 Work


Work is done only in
lifting the barbell.
The physics of a
weightlifter holding a
stationary barbell is no
different than the physics
of a table supporting a
barbell's weight. NO NET
FORCE acts on the barbell
(forces are balanced!!),
no work is done, and no
change in its energy
occurs.
Is This Work???
A
student applies a force to a
wall and becomes exhausted.
 A book falls off a table and lands
on the ground.
 You do some push-ups.
 A waiter carries a tray full of
meals across the room.
9.1 Work

The waiter does
NO work because
the object is NOT
moving in the
direction of the
force. (The force is
against gravity –
its in an up & down
direction.)
9.1 Work
 Mathematically,
work = force x
distance.
W = Fd
 The unit for work combines the unit
for force, N, with the unit for
distance, m.
 A N-m is also called a joule (J).
1 kJ equals 1000 J.
W=Fxd
Recall that when lifting an object against
gravity, the force required equals the
object’s weight.
 Fgrav = Weight = mg
 Therefore, W = mgd
 So, if the mass is doubled, the required
force and work are doubled.
 If the distance is doubled, the work is
doubled.
 Force (F) and distance (d) are both
directly proportional to work.

9.1 Work

There are 2 kinds of work.
1. Work done against another force
•
To pick up an object you do work against
gravity.
•
To push an object, you do work against
friction.
2. Work is done to change the speed of an
object.
•
Work is done to speed up or slow down a
car.

In either case, when work is done, a
transfer of energy occurs between an
object and its surroundings.
Practice
A weight lifter lifts a barbell. How much
work is done if he lifts a barbell that is
twice as heavy the same distance? If he
lifts a barbell that is twice as heavy and 2x
as far?
 If you apply a 50 N force to a package,
pushing it across the floor 3 m, how much
work do you do?
 A tugboat pulls a ship with a constant net
horizontal force of 5000 N. How much
work does the tugboat do on the ship if
each moves a distance of 3.00 km?

9.2 Power
When you climb a
staircase, you do
the same amount
of work whether
you get to the top
in 30 sec. or 2
minutes.
 What is different in
each case is how
fast the work is
done or the power.

9.2 Power
Power is the rate at which work is done.
 Power equals the amount of work done
divided by the time interval during which
the work is done: P = Fd = mgd
t
t

9.2 Power
 Power
= Work/Time. This means
power is directly proportional to work
and indirectly proportional to time.
 Having twice the power, then, can
mean several things.
Twice the work can be done in the same
amount of time.
The same work can be done in ½ the
time.
9.2 Power
The unit of power is the
joule per second or
watt (W).
 For historical reasons,
the horsepower is
occasionally used to
describe the power
delivered by a machine.
 One horsepower is
equivalent to
approximately 750
Watts.

To lift a ¼ lb. cheeseburger
a distance of 1 m in 1 s
requires 1 watt of power!
Practice



Two physics students, Will and Ben, are in the
weightlifting room. Will lifts the 100-pound
barbell over his head 10 times in one minute;
Ben lifts the 100-pound barbell over his head 10
times in 10 seconds. Which student does the
most work? Which student delivers the most
power?
If little Nellie Newton lifts her 40-kg body a
distance of 0.25 meters in 2 seconds, then what
is the power delivered by little Nellie's biceps?
Joe elevates his 80-kg body up the 2.0 meter
stairwell in 1.8 seconds. What is his power?
9.3 Mechanical Energy
 When
work is done on an object, the
object acquires the ability to do work
on something else.
For example, when you do work to lift a
hammer, the hammer now has the
ability to do work on a nail.
 The
property of an object that
enables it to do work is energy.
Energy is measured in joules.
9.3 Mechanical Energy
 Mechanical
energy is the energy due
to the position or movement of an
object.
 The 2 forms of mechanical energy
are kinetic energy and potential
energy.
9.4 Potential Energy
Energy that is stored
and held in readiness
is called potential
energy (PE).
 Stored energy has the
potential to do WORK.
 3 kinds of PE are:
elastic PE, chemical
PE, and gravitational
PE.

Elastic Potential Energy
A compressed or
stretched spring
has the potential to
do work.
 Other examples
include a stretched
rubber band or a
stretched string on
a bow and arrow.

Chemical Energy
Fuels (like oil or food)
have chemical
potential energy.
 This energy is
available to do work
when a chemical
reaction breaks the
bonds between the
atoms in a fuel and
thereby releases the
energy stored in them.

Gravitational Potential Energy
Work is required to elevate objects against
gravity. The lifted objects then have PEgrav.
 The work required (above) will be the same
in each case because the work is equal to
the force (weight of the object) times the
distance it is moved against gravity (3 m in
each case).

Gravitational Potential Energy
 The
amount of gravitational PE
possessed by an elevated object is
equal to the work done in lifting it.
PEgrav = Fd
Since F = weight & weight = mg,
PEgrav = mgh
(where h = height or distance lifted)
Gravitational Potential Energy



The height is the
distance above a
chosen reference level.
Often this reference
level is the ground or
floor.
A book on a table will
have no height relative
to the table and no PE.
It does, however, have
a positive PE relative to
the floor.
Uses of PEgrav


Hydroelectric power
makes use of the
gravitational potential
energy of water.
Falling water drives a
turbine, which is
connected to a
generator. The
generator converts the
energy from the falling
water into electrical
energy.
Practice

Knowing that the potential energy at the
top of the tall pillar is 30 J, what is the
potential energy at the other positions
shown on the hill and the stairs.
Practice
 If
a force of 15 N is used to lift a load
to height 3 m from the ground, what
is the PE of the load?
 A 10 kg mass is suspended 5 m from
the ground.
How much work was done to the mass?
If it is lifted in 2 sec., how much power
is expended?
What is the PEgrav of the mass?
9.5 Kinetic Energy



If an object is moving, it is capable of doing
work.
It has energy of motion or kinetic energy (KE).
The amount of kinetic energy which an object has
depends upon two variables:
 the mass (m) of the object
 the speed (v) of the object.
KE =
2
½mv
9.5 Kinetic Energy
 The
kinetic energy of a moving
object is equal to the work required
to bring it to its speed from rest or to
the work it can do while it is being
brought to rest.
KE = W
1/2mv2 = Fd
1/2mv2 = Fd
What this means:
– If the speed of a vehicle
is doubled, its KE is
quadrupled.
– So, 4x as much work
must be done to stop the
vehicle.
– If the braking force used
to stop the vehicle is the
same, the distance
required for stopping will
be 4x as great.

What if the speed is
tripled?
Types of Kinetic Energy
Thermal energy
 Sound
 Light
 Electricity

Kinetic Energy
Kinetic energy often appears “hidden” in
one of its different forms, such as heat,
sound, light, and electricity.
• Random molecular motion is sensed
as heat.
• Sound consists of molecules
vibrating in rhythmic patterns.
• Light energy originates in the motion
of electrons within atoms.
• Electrons in motion make electric
currents.
Practice
Determine the kinetic energy of a 1000-kg
roller coaster car that is moving with a speed
of 20.0 m/s.
 If the roller coaster car in the above problem
were moving with twice the speed, then
what would be its new kinetic energy?
 Alison, a platform diver for the Ringling
Brother's Circus, has a kinetic energy of
15,000 J just prior to hitting a bucket of
water. If Alison’s mass is 50 kg, then what is
her speed?

9.6 Work-Energy Theorem
 The
work-energy theorem
describes the relationship between
work and energy: whenever work
is done, energy changes.
 Work = ΔKE
9.6 Work-Energy Theorem

Work equals change in KE.
 If you push on a box and it does not slide,
then no work is done on the box.
 If there is no friction, the box will slide. The
force and distance of your push will be the KE
of the box. (If there is some friction, the net
force is what is considered.)
 If the box has a constant speed, your push is
just enough to overcome friction. Since the
net force is 0, work is 0 and there is no change
in KE of the box.
9.6 Work-Energy Theorem


The more KE an object
has, the more work
must be done to stop
it.
This infrared shot of a
tire shows that some
of the KE of a vehicle
was transferred into
thermal energy of the
tire when the vehicle
was stopped.
9.6 Work-Energy Theorem




Recall our skidding
example from a previous
slide.
The maximum braking
force that brakes supply is
independent of speed – it
is nearly always the same.
Therefore, a car moving at
twice the speed has 4x as
much KE. It will take 4x
as much distance to stop.
Distances may be even
greater if a driver’s
reaction time is taken into
account.
9.7 Conservation of Energy
Nearly every process
in nature can be
analyzed in terms of
transformations of
energy from one form
to another.
 In this toy car, for example, work is done to
wind it up. The car then has elastic
potential energy. When released, it is
converted into kinetic energy and heat.
 Energy changes from one form to another,
without a net loss or gain.

9.7 Conservation of Energy

The law of conservation of energy states that energy
cannot be created or destroyed. It can be
transformed from one form into another, but the
total amount of energy never changes.
9.7 Conservation of Energy
In a swinging pendulum system, there is one
quantity that does not change: the total energy
of the system. Due to friction, energy will
eventually be transformed into heat.
9.7 Conservation of Energy
Energy changes from one form to another but the
total amount of energy remains the same. In this
example, the total amount of energy can also be
called the total mechanical energy.
Practice
1. As the object moves from
point A to point D across the
surface, the sum of its
gravitational potential and
kinetic energies ____.
a. decreases only
b. decreases and then increases
c. increases and then decreases
d. remains the same
2. The object will have a minimum gravitational potential
energy at point ____.
a. A b. B c. C d. D e. E
3. The object's kinetic energy at point C is less than its kinetic
energy at point ____.
a. A only b. A, D, and E c. B only d. D and E
Practice
0 m/s
9.8 Machines



A machine is a device that is used to multiply or
change the direction of forces.
Based on the law of conservation of energy, a
machine cannot put out more energy than is put
into it.
What a machine can do is transfer energy from
one place to another or transform it from one
form to another.
Levers
A lever is a simple
machine made up of a
bar that turns about a
fixed point.
 The fixed point is
called the fulcrum.
 A lever changes the
direction of a force –
when the lever is
pushed down, the
load is lifted up.

Levers
If we neglect friction:
work input = work output
 Since work = Fd,
(Fd)input = (Fd)output
 On one end of this lever, a
small input force is exerted
over a large distance.
 This produces, on the other
end of the lever, a large
force exerted through a
short distance.
 This machine has
multiplied the force (but
not the work)!

Note: in this lever, the
fulcrum is relatively close
to the load.
Mechanical Advantage
Consider an ideal
example: the girl
pushes with a force of
50 N and lifts a load
of 5000 N.
 The ratio of Foutput to
Finput for a machine is
called the mechanical
advantage.
 Foutput =5000 N = 100
Finput
50 N

Mechanical Advantage
MA = Foutput = 100
Finput
 Notice that doutput is
1/100th of dinput.
 This means,
mechanical advantage
can also be calculated
using the distances:

MA = dinput
doutput
Types (or Classes) of Levers
A type 1 lever has the
fulcrum between the
input and output
forces.
 Examples include:

Types of Levers
In a type 2 lever, the
output force (the
load) is between the
fulcrum and the input
force (the effort).
 In this lever, the
forces have the same
direction.
 Examples include:
staplers, bottle
openers, nut
crackers, and

Types of Levers
In a type 3 lever, the
fulcrum is at one end
and the output force
(the load) is at the
other. The input force
(the effort) is between
them.
 In this lever, the
forces have the same
direction.
 Examples include:
your biceps and

Pulleys




A pulley is a kind of
lever that can be used
to change the direction
of a force.
This single pulley is like
a type 1 lever – the
fulcrum (pulley axis) is
between the input and
output forces.
Someone pulls down on
the rope and the load is
lifted up.
The MA of this type of
pulley is 1: Finput = Foutput
( & dinput = doutput)
Pulleys




This single pulley acts as a
type 2 lever - the load is
between the input force
and the fulcrum (ropepulley contact point).
Pulling up on the rope lifts
the load up.
The MA of this pulley is 2:
a 2N load can be lifted
with a 1N force; the rope
will be pulled 2 m for
every 1 m the load is
lifted.
An easy way to determine
MA is to count the number
of ropes that support the
load: 2!
Pulleys
The MA for pulley
systems is the same
as the number of
strands that support
the load.
 In this diagram, there
are 5 strands of rope
but only 4 support the
load. The MA, then, is
4.
 Calculated: MA =
Foutput = 100 = 4
Finput
25

Practice
 If
a pulley can lift a 500 N load with
a force of 100 N, what is its MA?
 A lever is pushed downward a
distance of 1m. As a result, a load is
lifted up 1/8 m. What is the MA of
this lever?
 John’s biceps contract 1 cm to lift a
10 N load a distance of 10 cm. What
is the MA of his biceps?
9.9 Efficiency
 In
our IDEAL examples,
Winput = Woutput
IDEAL machines have 100% efficiency.
 REAL machines are not 100%
efficient. In REAL machines, some
input energy is used to overcome
frictional forces and is converted into
thermal energy.
9.9 Efficiency
The efficiency of a machine is the ratio of
useful energy output to total energy input.
It is often expressed as a percentage.
 E = useful Woutput x 100
total Winput
 If you do 50 J of work on a lever and get
out 42 J of work, the efficiency of the lever
is: 42J x 100 = 0.84 or 84%.
50J

 8 J of your work is “lost” to heat.
 The lower the efficiency, the greater the amount
of energy that is wasted.
Practice Problems
1.
2.
Using a lever, a person applies 60 N
of force and moves the lever by 1
m. This moves the 200 N rock at
the other end by 0.2 m. What is
this machine’s efficiency?
A person in a wheelchair exerts a
force of 25 N to go up a ramp that is
10 m long. The weight of the
person and wheelchair is 60 N and
the height of the ramp is 3 m.
What is the efficiency of this
Inclined Plane
This machine is
generally used to
elevate heavy loads.
Less force is required
(Finput) to slide a load
up an incline than is
required to lift it
vertically (Foutput).
 Recall that MA = dinput
doutput
 MA = 6m/3m = 2
 This is an IDEAL (or
theoretical) MA , the
IMA.

Inclined Planes
However, inclined
planes do not have
efficiency’s of 100%.
Some of the work done
to go up a ramp, for
example, is “lost” to
the ramp through
friction. Actual MA is
much less than
theoretical MA (IMA).
 AMA = Foutput
Finput

Inclined Planes



Efficiency can also be expressed as a
ratio of actual MA to ideal MA.
E = actual MA
x 100
ideal MA
Practice:
1. If an inclined plane has a theoretical MA of 2
but an actual MA of 1.8, what is its
efficiency?
2. A pulley has an IMA of 6 and an AMA of 5.
What is its efficiency?
Complex Machines

Inclined plane

An auto jack is a
combination of 2 simple
machines – a lever and
an inclined plane
wrapped around a
cylinder. Turning the
handle raises the load a
distance of 1 pitch (the
distance between ridges).
The theoretical MA of a
jack is very high;
however, the efficiency is
only about 20%. Actual
MA approximates 100.
Complex Machines
 Automobile
engines are also complex
machines.
 In the engine, the chemical energy
of a fuel is released when the fuel is
burned. Much of the energy (65%)
released is transformed into thermal
energy; the remainder is
transformed into the mechanical
energy used to run the engine.
9.10 Energy for Life
Cells are machines and need a supply of
energy. They use the energy stored in
hydrocarbons (like glucose). The energy
is released during respiration (a reaction
of the fuel with oxygen).
 There is more energy stored in the
molecules of food than is stored in the
products of food metabolism. This energy
difference is used to sustain life.
 Metabolism is like the burning of fuel in an
engine. The difference is the rate of
energy release. Reaction rates in
metabolism are very slow.

9.11 Sources of Energy
The SUN is the source
of nearly all our energy
on Earth.
 Plants use sunlight
during photosynthesis
to produce
hydrocarbon
compounds. These
compounds become
our wood, fossil fuels
and our food.

Solar Power
SOLAR POWER takes
sunlight and
converts it directly
into electricity by
using photovoltaic
cells.
 Indirectly, the sun
powers the water
cycle; here falling
water can turn
generator turbines
and generate
electricity.

Solar Power

Wind power is
another indirect
form of solar
power. Wind,
caused by the
unequal heating of
the Earth’s surface,
can be used to turn
generator turbines
in special
windmills.
Fuel Cells
 Much
is being done today to use
hydrogen as a fuel. When it is
burned, water vapor is the only
product.
 Hydrogen is NOT a source of energy,
however, because it must be “made”
from water and carbon compounds.
This requires energy.
Fuel Cells
Electricity is used to split
water molecules into
hydrogen and oxygen in
a process called
electrolysis.
Fuel cells makes the
electrolysis process run
in reverse. Water is
produced and electric
current is generated.
Nuclear and Geothermal Energy



Nuclear fuels, like
uranium and plutonium,
are the most
concentrated forms of
usable energy.
Radioactivity from such
fuels keeps the Earth’s
interior hot.
Geothermal energy is
held in underground
reservoirs of hot water.
They can be tapped to
provide steam for
running generator
turbines.