Transcript Chapter 7: Machines, Work, and Energy

Energy and Systems
Unit 3: Energy and Systems
Chapter 7: Machines, Work, and Energy
 7.1
Work, Energy and Power
 7.2
Simple Machines
 7.3
Efficiency
7.1 Investigation: Force, Work, and Machines
Key Question:
How do simple machines
affect work?
Objectives:
Build a simple machine that multiplies force.
 Measure and compare input and output forces and distances
for different pulley setups.


Calculate and compare work input and work output.
Work

Doing work always means transferring
energy.

The energy may be transferred to the
object to which you apply the force, or it
may go elsewhere.

The work you do in stretching a rubber
band is stored as potential energy by the
rubber band.

The rubber band can then use the energy
to do work on a paper airplane by giving it
kinetic energy.
Doing work
 To
do the greatest amount of work, you must apply
force in the same direction the object will move.
 If
forces A, B, and C have equal strengths, force C
will do the most work because it is entirely in the
direction of the motion.
Work done against gravity
 Many
situations involve work
done by or against the force
of gravity.
 It
does not matter whether
you lift an object straight up or
you carry it up the stairs.
 The
total work done against
gravity is the same no matter
what path you take.
Work done against gravity
mass (g)
work (joules)
W = mgh
height object raised (m)
gravity (m/sec2)
Calculating work
Alexander has a mass of 70 kilograms. His apartment is on the
second floor, 5 meters up from ground level. How much work does
he do against gravity each time he climbs the stairs to his
apartment?
1. Looking for: …work.
2. Given: … mass (70 kg) and height (5 m). You know that
g = 9.8 m/s2.
3. Relationships: Use: Fg = mg and W = Fd
4. Solution: The force is equal to Alexander’s weight.
Fg = (70 kg)(9.8 m/s2) Fg = 686 N
Use the force to calculate the work.
W = Fd W = (686 N)(5 m) W = 3,430 J
Work Energy Theorem

The work-energy theorem says that the work done by a
system equals the change in kinetic energy of that system.

To understand how work and kinetic energy are related, let’s
suppose a ball of mass (m) is at rest.

A force (F) is applied and creates an acceleration (a).

After moving a distance (d), the ball has reached a speed (v).
Work Energy Theorem
1.
The work done on the ball is its mass times
acceleration times distance.
2.
When an object starts from rest, you can relate
distance traveled, acceleration, and time using the
formula that includes all three.
Work Energy Theorem
3.
4.
Using this relationship, you can replace distance in
the equation for work and combine similar terms.
Mathematically, v = at, therefore v2 = a2t2.
Calculating kinetic energy
A car with a mass of 1,000 kg is going straight ahead at a speed of 10
m/s. The brakes can supply a force of 10,000 N. Calculate:
a) the kinetic energy of the car.
b) the distance it takes to stop.
1.
2.
3.
4.
Looking for: … kinetic energy and distance to stop the car.
Given: … mass (1,000 kg), speed (10 m/s) and force
(10,000 N).
Relationships: Use equations: Ek = mv2 and W = Fd
Solution: Ek = (1,000 kg)(10 m/s)2 = 50,000 J
To stop the car, work done by the brakes reduces the Ek to
zero.
50,000 J = (10,000 N) × d
d = 5 meters
Power
 The
 It
rate at which work is done is called power.
makes a difference how fast you do work.
 The
unit for power is equal to the unit of work
(joules) divided by the unit of time (seconds).
Power
 Michael
and Jim do the
same amount of work.
 Michael’s
power is
greater because he gets
the work done in less
time.
 To
find Michael’s power,
divide his work (200 J) by
his time (1 s).
Power
 James
Watt, a Scottish
engineer, invented the
steam engine.
 James
Watt explained
power as the number of
horses his engine could
replace.
 One
horsepower still
equals 746 watts.
Calculating power
A roller coaster is pulled up a hill by a chain attached to a motor.
The roller coaster has a total mass of 10,000 kg. If it takes 20s to
pull the roller coaster up a 50 m hill, what is the power produced
by the motor?
1.
Looking for: … power of the motor.
2.
Given: … mass (10,000 kg), time (20 s), and height (50 m).
3.
Relationships: Use: Fg = mg
4.
W = Fd
P = W/t
Solution: Calculate the weight of the roller coaster:
Fg = (10,000 kg)(9.8 m/s2) = 98,000 N
Calculate the work:
W = (98,000 N)(50 m) = 4,900,000 J or 4.9 × 106 J
Calculate the power:
P = (4.9 × 106 J) (20 s) = 245,000 W or 2.45 × 105 W
Unit 3: Energy and Systems
Chapter 7: Machines, Work, and Energy
 7.1
Work, Energy and Power
 7.2
Simple Machines
 7.3
Efficiency
7.2 Investigation: Work and Energy
Key Question:
How does a system get energy?
Objectives:

Use force and distance data gathered during experiments to
create graphs; and, then analyzethe data and graphs to
calculate work.

Derive the formula for the speed of a car from force and mass
data.

Analyze data to determine the relationship between the work
done by a force and the energy of a body.
Using Machines
 A machine
is a device with
moving parts that work
together to accomplish a
task.
 A bicycle
is a good example.
Using Machines
 The
input includes everything you do to make the
machine accomplish a task, like pushing on the
bicycle pedals.
 The
output is what the machine does for you, like
going fast or climbing a steep hill.
Forces in Machines
 A simple
machine is an unpowered mechanical
device, such as a lever.
Mechanical advantage
 Machines
multiply forces.
 The
mechanical
advantage of a machine is
the ratio of the output force
to the input force.
 One
person could lift an
elephant—quite a heavy
load—with a properly
designed system of ropes
and pulleys!
Calculating mechanical advantage
What is the mechanical advantage of a lever that allows Jorge to lift
a 24-newton box with a force of 4 newtons?
1.
Looking for: … mechanical advantage.
2.
Given: … input force (4 N) and the output
force (24 N)
3.
Relationships: Use: MA = Fo ÷ Fi
4.
Solution: MA = (24 N) ÷ (4 N)
MA = 6
Work and Machines
 A rope
and pulley machine
illustrates a rule that is true
for all processes that
transform energy.
 The
output work done by a
simple machine can never
exceed the input work done
on the machine.
Calculating mechanical advantage
A jack is used to lift one side of a car in order to replace a tire. To
lift the car, the jack handle moves 30 cm for every 1 cm that the car
is lifted. If a force of 150 N is applied to the jack handle, what force
is applied to the car by the jack? You can assume all of the input
work goes into producing output work.
1.
Looking for: … output force in newtons.
2.
Given: … input force (150 N), input distance (30 cm = .03 m) and output
distance (1 cm = .01 m)
3.
Relationships: Use: Work = Fd and
Input work (Wi) = Output work (Wo)
4.
Solution: Wi = (150 N)(0.30 m) = 45 J = Wo
Wo = 45 J = F × 0.01 m
F = 45 J ÷ 0.01 m = 4,500 N
How a lever works
 A lever
includes a stiff structure (the lever) that
rotates around a fixed point called the fulcrum.
The Lever
 Levers
are useful because you can arrange the
fulcrum and the input arm and output arm to
adjust the mechanical advantage of the lever.
Three types of levers
 The
three types of levers are
classified by the location of the
input and output forces relative
to the fulcrum:
— first class lever
— second class lever
— third class lever
Calculating the position of the
fulcrum
A lever has a mechanical advantage of 4. Its input arm is
60 cm long. How long is its output arm?
1.
Looking for: … length of output arm.
2.
Given: … mechanical advantage (4) and input arm length
(60 cm)
3.
Relationships: Use: MA = Li ÷ Lo
4.
Solution: 4 = 60 cm ÷ Lo
Lo = 60 cm ÷ 4 = 15 cm
Tension in ropes and strings
 Recall
that ropes and strings carry tension forces
along their length.
 If
the rope is not moving, its tension is equal to the
force pulling on each end.
Rope & Pulleys

The block-and-tackle machine
is a simple machine using one
rope and multiple pulleys.

The rope and pulleys can be
arranged to create different
amounts of mechanical
advantage.
Gears
 Many
machines require that
rotating motion be
transmitted from one place to
another.
 Gears
speed.
change force and
Designing Gear Machines

The gear ratio is the ratio of output
turns to input turns.

You can predict how force and speed
are affected when gears turn by
knowing the number of teeth for
each gear.
Turns of output gear
Turns of input gear
To = Ni
Ti
No
Number of teeth
on input gear
Number of teeth
on input gear
Ramps
 A ramp
is a simple machine that allows you to
raise a heavy object with less force than you
would need to lift it straight up.
Ramps
 The
mechanical
advantage of a ramp is
the ramp length divided
by the height of the ramp.
Screws
 A screw
is a rotating
ramp.
 You
find the mechanical
advantage of a screw by
dividing its circumference
by the lead.
Unit 3: Energy and Systems
Chapter 7: Machines, Work, and Energy
 7.1
Work, Energy and Power
 7.2
Simple Machines
 7.3
Efficiency
7.3 Investigation: Energy and Efficiency
Key Question:
How well is energy transformed
from one form to another?
Objectives:
Explain the meaning of efficiency and describe why processes
are not 100 percent efficient.
 Describe the energy conversions involved as the Energy Car
travels along the SmartTrack and collides with a rubber band.
 Explore the effects of changing variables, such as mass and
tension, on the efficiency of a process.

Efficiency
Every process that is done by machines can be simplified in
terms of work:
1.
Work input: the work or energy supplied to the process (or
machine).
2.
Work output: the work or energy that comes out of the
process (or machine).
Efficiency and Friction
 Friction
is a force that opposes
motion.
 Friction
converts energy of motion
to heat.
 It
is important to remember that
the energy does not disappear.
 Energy
is converted to other forms
of energy that are not always
useful.
Efficiency
 A machine
would have an
efficiency of 100 % if the
work output of the machine
is equal to the work input.
 A machine
What percentage of the
energy is “lost” due to
friction?
that is 75 %
efficient can produce three
joules of output work for
every four joules of input
work
Efficiency
 The
efficiency of a machine is the ratio of usable
output work divided by total input work.
 Efficiency is usually expressed in percent.
Output work (J)
Efficiency = Wo
Wi
Input work (J)
x 100%
Efficiency and time
 The
efficiency is less
than 100 percent for
virtually all processes
that convert energy to
any other form except
heat.
 Scientists
believe this is
connected to why time
flows forward and not
backward.
Time runs forward


Once energy is transformed
into heat, the energy cannot
ever completely get back
into its original form.
Because 100 % of the heat
energy cannot get back to
potential or kinetic energy,
any process with less than
100 percent efficiency is
irreversible.

Irreversible processes can
only go forward in time.

Since processes in our
universe almost always lose
a little energy to friction, time
cannot run backward.
Electric Wind

In a library textbook called
Explaining Physics, fourteen
year old William Kamkwamba
read that if you spin a coil of
wire inside a magnetic field, an
electric current is created.

An idea began to take shape in
William’s mind.

If he could build a windmill, he
could have light in the evenings!