Transcript Chapter 6

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Chapter 6
Work and Machines
6.1
Work vs. Impulse
It takes Energy to push something and make it
move.
• 2 conditions
1.) Force Exerted.
2.) How long force is exerted.
For…
Impulse = “how long” means time.
Work = “how long” means distance
What is Work?
Work makes something move!
• Work-the transfer of energy that occurs
when a force makes an object move.
• 2 conditions
1.) Force must make the object move.
2.)Movement must be in the same direction as
force.
Is this work?
Examples:
Lifting a barbell?
Holding a barbell steady?
Carrying barbell across the gym?
• Why?
Formula to calculate work
Work(J)=Force(N)*distance (m)
Or: W= Fd
Try this!
Alexander has a mass of 70 kg. His
apartment is on the second floor, 5
meters from the ground level. How
much work does he do against
gravity each time he climbs the
stairs to his apartment?
1. W=fd
2. W= (70 kg x 10 m/s2) (5 m)
3. W= 3500 J
Try this!
How much additional work does
Alexander have to do if he is
carrying 5 kg of groceries?
1. W=fd
2. W= (75 kg x 10 m/s2) (5 m)
3. W= 3750 J
Try this!
A car engine does 50,000 J of work to
accelerate at 10 m/s2 for 5 m.
What is the mass of the car?
1. F = W ÷ d
2. F = 50,000 J ÷ 5 m
3. F = 10,000 N
4. F = m x a
5. 10,000 N = 10 m/s2 x m
6. Mass = 1000 kg
POWER!
Power-amount of work done in one
second.
• Rate at which work is done
• SI unit = Watts (W)
• 1 kilowatt = 1000 W
Formula
Power (Watts) = Work (Joules) /
Time(seconds)
P = W/t
Problem
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 20 s to pull the
roller coaster up a 50 m hill, how
powerful is the motor?
• P = W/t; W = Fxd
• W = (10,000 kg x 10 m/s2) x 50 m
• P = 5,000,000 J ÷ 20 s = 250 kW
ANOTHER PROBLEM…
What would the motor’s power be if it
took 40 s to pull the same roller
coaster up the hill?
P = W/t
P = 5,000,000 J / 40 s
P = 125 kW
YET ANOTHER PROBLEM…
What is the power of a 70 kg person
who climbs a 10-meter high hill in 45
s?
P = W/t; W=Fd
P = (70 kg x 10 m/s2) x 10 m / 45 s
P = 156 W
TIEING IT ALL TOGETHER
Power is also the rate at which energy is
transferred.
Power (Watts) = Energy transferred (Joules)
time (seconds)
P= E/t
EX: Power used by lightbulb is the amount
of electrical E used each second.
Work and Energy
Energy-the ability to cause change or to do
work
Types of energy:
Potential = energy of position.
m x g x h or F x h.
Kinetic = energy of motion
½ m x v2
• transfer of energy always occurs when
work is done!
Mechanical Energy
Includes both Potential and Kinetic
Energy
The sum of the kinetic and potential
energy in a system.
Work – Energy Theorem
Work is equal to change in Energy
(could be potential or kinetic)
Work = ΔKE or ΔPE
Work – Energy Theorem
Energy is required to change the
motion of an object (speed up or
slow down)
The more motion an object has, the
more KE the object has.
Work = Δ KE, therefore the more KE
the more work required to change
the object’s motion.
Work and Energy
 Height of the
weight, Δ y =
distance the tractor
travels, d.
 Ideal situation:
constant speed
and negligible
friction - therefore
Ftractor = Fweight
 PE is given by FΔ y,
& Wtractor on the
weight equals Fd
 So W = ΔE
Try this!
How much work is needed to lift an
object that weighs 500 N to a
height of 4 m? How does this work
compare to the change in PE for
that object?
1. W=fd or PE = m x g x h
2. W= (500N) (4m) or PE = 500 N x 4 m
3. W= 2000 J or PE = 2000 J
4. They are the same!
Try this!
A tractor accelerates a 100 kg trailer from
rest to a velocity of 5 m/s over a
distance of 1.25 m. How much work is
required and how does this work
compare to the change in KE for that
object? What is the acceleration of the
trailer?
1. W=fd or KE = ½ m x v2
2. W= (100 kg x 10 m/s2) (1.25 m)
or KE = ½ 100 kg x 52
3. W= 1250 J or KE = 1250 J
4. They are the same!
5. F = ma; a = 10 m/s2
Try this!
A car traveling along a level road at speed
“v” slams on the brakes and skids to a
stop. If the force of friction on the car is
half the car’s weight, how far does the
car slide?
1. W=Fd or ΔKE = ½ m x v2
2. Fd = ½ m v2
3. d = ½ m v2 ÷ F; F = ½ m g
4. d = v2 ÷ g
5. Stopping distance is proportional to v2
6.8
Machines
Machine- a device that makes
doing work easier.
•  force that can be applied on an object.
•  the distance over which a force can be
applied.
• Changing the direction of the force applied
Work done by Machines
Input force-force that is applied to the
machine. Fin
Output force- force applied by the
machine. Fout
Conserving Energy
Energy is always conserved!
• Your energy is transferred to machine
• Machine transfers energy to the object.
• Some energy changes to heat due to
friction
•Wout is never greater than Win
Work done by Machines
If Friction is negligible, meaning not
present, then we can say the
following:
Work input = Work output
(Fd)in = (Fd)out
Simple Machines
• 6 classes of machines:
Lever
Inclined plane
Pulley
Wheel & axle
Wedge
Screw
1. Lever
Lever- A bar that is free to pivot or turn
around a fixed point.
Parts of a Levers
Fulcrum- fixed point
Input Arm- Distance from fulcrum to
part where input force is applied.
( E =effort force)
Output arm-Distance from fulcrum to
part where output force is applied.
(R =resistance Force)
First Class levers
INPUT FORCE
OUTPUT FORCE
• Fulcrum is
between the
output ( R ) &
input force (E).
• Forces move in
opposite
directions
• Ex: See saw
Second Class Levers
OUTPUT FORCE
FULCRUM
• Output force
between the input
force & fulcrum.
• EX: Car door,
wheelbarrow
INPUT FORCE
Third Class Lever
OUTPUT FORCE
INPUT FORCE
FULCRUM
• The input force is
between output
force and fulcrum.
• EX: Your arm,
hockey stick,
baseball bat.
Mechanical Advantage
Mechanical advantage-the ratio of
the output force to the input force
MA = output force (N)
input force (N)
• The mechanical advantage of a machine
without friction is the ideal mechanical
advantage. (IMA)
Ideal MA (lever)
IMA= Length of input arm (m)
Length of output arm (m)
IMA = Linput ÷ Loutput
Example Problem
A lever has a mechanical advantage
of 4. Its input arm is 60 cm long.
How long is its output arm?
1. MA = Lin ÷ Lout
2. 4 = 60 ÷ Lout
3. Lout = 15 cm
Example Problem
What is the mechanical advantage of
a lever with an input arm of 25 cm
and an output arm of 100 cm?
1. MA = Lin ÷ Lout
2. MA = 25 cm ÷ 100 cm
3. MA = 0.25
Example Problem
A lever has an input arm of 100 cm and an
output arm of 10 cm. What is the
mechanical advantage of this lever?
Given the mechanical advantage, how
much input force is needed to lift a 100-N
load?
1. MA = Lin ÷ Lout
2. MA = 100 cm ÷ 10 cm = 10
4. MA = Fout ÷ Fin; 10 = 100-N ÷ Fin
5. Fin = 10 N
Example Problem
You want to use a lever to lift a 2000 N
rock. The maximum force you can
exert is 500 N. Draw a lever that will
allow you to lift the rock. Label the
input force, output force, fulcrum,
input arm and output arm. Specify
measurements for the input and
output arms.
2. Pulleys
Pulley – grooved wheel w/ a rope or chain,
or cable running along a groove.
 Modified 1st class lever
 Can change direction of input force or
increase output force
 Three types!
PULLEYS
1. Fixed PulleyChanges
only
direction of
force.
 IMA = 1
EX: Elevator
cable
FULCRUM
PULLEYS
2. Moveable pulley- one end of the rope is
fixed & wheel is free to move.
 Multiplies force  Force required =
weight
÷ IMA
String attached to
ceiling is another
person who can
support ½ weight of the
load.
Output force = 8 N
Input force = 4 N
IMA = 2
8N
If the weight of
the load is
equal to 8 N,
you only need
to exert a
force of 4 N in
order to
support and lift
the load.
PULLEYS
3. Block & Tackle- System of fixed & moveable
pulleys
IMA= # of ropes that support the weight.
Force required = weight ÷ IMA
IMA = 2
Fixed Pulley
Moveable Pulley
Efficiency
Efficiency- a measure of how much of the
work put into a machine is changed into
useful output work by the machine.
efficiency ( %) = output work (J)
input work (J)
X 100
•  Efficiency by reducing friction
– Lubrcant ex: oil or grease, ball bearings,
etc…
Work & Energy
Work - the transfer of energy that occurs
when a force makes an object move.
• 2 conditions
1.) Force must make the object move.
2.)Movement must be in the same
direction as force.
W=Fxd
Work & Energy
Work - the transfer of energy that occurs
when a force makes an object move.
Types of energy:
Potential = energy of position.
m x g x h or F x h.
Kinetic = energy of motion
½ m x v2
Work must equal CHANGE IN ENERGY!
Work & Energy
Power-amount of work done in one
second.
• Rate at which work is done
Formula
P = W/t
Work & Energy
Machine- a device that makes
doing work easier.
•  force that can be applied on an object.
•  the distance over which a force can be
applied.
• Changing the direction of the force
applied
• Win = Wout or (Fd)in = (Fd)out
Simple Machines
• 6 classes of machines:
Lever
Inclined plane
Pulley
Wheel & axle
Wedge
Screw
Mechanical Advantage
Mechanical advantage-the ratio
of the output force to the input
force
MA = output force (N)
input force (N)
MA lever = Lin/Lout
MA pulley = # ropes supporting weight
Efficiency
Efficiency- a measure of how much of the
work put into a machine is changed into
useful output work by the machine.
efficiency ( %) = output work (J)
input work (J)
•  Efficiency by reducing friction
X 100