Transcript File - Mrs. Ellis` Science Class!

Machines - Ch. 12
Introduction to Machines
Work,
Power, Energy
Mechanical Advantage
Simple Machines
Compound Machines
Work
 Work
 transfer of energy through motion
 force exerted through a distance
W = Fd
W:
F:
d:
work (J)
force (N)
distance (m)
1 J = 1 N·m
Distance must be in direction of force!
B. Work

Brett’s backpack weighs 30 N. How much
work is done on the backpack when he lifts it
1.5 m from the floor to his back?
GIVEN:
F = 30 N
d = 1.5 m
W=?
WORK:
W = F·d
W = (30 N)(1.5 m)
W = 45 J
W
F d
B. Work

A dancer lifts a 40 kg ballerina 1.4 m in the air and
walks forward 2.2 m. How much work is done on
the ballerina during and after the lift?
GIVEN:
m = 40 kg
d = 1.4 m - during
d = 2.2 m - after
W=?
W
F d
WORK:
W = F·d
F = m·a
F =(40kg)(9.8m/s2)=392 N
W = (392 N)(1.4 m)
W = 549 J during lift
No work after lift. “d” is not in
the direction of the force.
Power
 Power
 Rate at which work is done; how
much work done in a given time
W=Pt
W:
P:
t:
work (J)
Power (Watt)
time (s)
1 J = 1 N·m
Distance must be in direction of force!
Power

It takes 100 kJ of work to life an elevator 18 m.
If this is done in 20 s, what is the average power
of the elevator during the process?
GIVEN:
W = 100 kJ
P=?
t =20 s
WORK:
P = W÷t
P = (100000 J)÷(20)
P = 5000 W
W
P t
Energy
THERMAL
The ability to
cause change.
internal motion of
particles
MECHANICAL
NUCLEAR
ENERGY
motion of objects
changes in the
nucleus
ELECTRICAL
CHEMICAL
bonding of atoms
joules (J)
motion of electric
charges
A. Energy
 Kinetic Energy (KE)
 energy in the form of motion
 depends on mass and velocity
• Which has the most KE?
80 km/h truck
• Which has the least KE?
50 km/h motorcycle
80 km/h
50 km/h
80 km/h
Kinetic Energy
KE = ½
2
mv
 Kinetic energy depends on
speed more than mass
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
KE = ½
WORK:
KE = ½ (m) (v)2
KE = ½ (44) (31)2
KE = 2.1 x 104 J
2
mv
A. Energy
 Potential Energy (PE)
 stored energy
 depends on position or
configuration of an object
• Which boulder has greater
gravitational PE?
• What other ways can an
object store energy?
Potential Energy
PE = mgh
 m=mass, g=free-fall acceleration,
h=height
 g on earth=9.8 m/s2
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
WORK:
GIVEN:
PE = mgh
PE = ?
PE = (65)(9.8)(35)
m = 65 kg
PE = 2.2 x 104 J
g =9.8 m/s2
h= 35 m

PE = mgh
C. Conservation of Energy
 Law of Conservation of Energy
 Energy may change forms, but it
cannot be created or destroyed
under ordinary conditions.
 EX:
 PE  KE
 mechanical  thermal
 chemical  thermal
C. Conservation of Energy
PE  KE
View pendulum animation.
View roller coaster animation.
C. Conservation of Energy
Mechanical  Thermal
View rolling ball animations.
View skier animation.
A. Machines
 Machine
 device that makes work easier
 changes the size and/or
direction of the exerted force
B. Force
 Effort Force (Fe)
 force applied to the machine
 “what you do”
 Also called Input Force
 Resistance Force (Fr)
 force applied by the machine
 “what the machine does”
 Also called Output Force
C. Work
 Work Input (Win)
 work done on a machine
Win = Fe × de
 Work Output (Wout)
 work done by a machine
Wout = Fr × dr
C. Work
 Conservation of Energy
 can never get more work out
than you put in
 trade-off between force and
distance
Win = Wout
Fe × de = Fr × dr
C. Work
 In an ideal machine...
Win = Wout
 But in the real world…
 some energy is lost as friction
Win > Wout
D. Mechanical Advantage
 Mechanical Advantage (MA)

number of times a machine
increases the effort force
Fr
MA 
Fe
• Fr=resistance force
•How much force the
object has
•Fe=Effort Force
•How much force you
use
MA > 1 : force is increased
 MA < 1 : distance is increased
 MA = 1 : only direction is changed

D. Mechanical Advantage
 A worker applies an effort force of 20 N
to open a window with a resistance force
of 500 N. What is the crowbar’s MA?
GIVEN:
WORK:
Fe = 20 N
Fr = 500 N
MA = ?
MA = Fr ÷ Fe
MA = (500 N) ÷ (20 N)
MA = 25
Fr
MA Fe
D. Mechanical Advantage
 Find the effort force needed to lift a
2000 N rock using a jack with a
mechanical advantage of 10.
GIVEN:
WORK:
Fe = ?
Fr = 2000 N
MA = 10
Fr
Fe = Fr ÷ MA
Fe = (2000 N) ÷ (10)
Fe = 200 N
MA Fe
D. Mechanical Advantage
 If you do NOT have forces give,
you can solve using distance
De
MA 
Dr



• De=distance of effort (in
meters)
•What you do
•Dr=Distance of
resistance (in meters)
•What machine does
MA > 1 : force is increased
MA < 1 : distance is increased
MA = 1 : only direction is changed
D. Mechanical Advantage
 Using a block and tackle pulley, a boy
pulls the rope 10 meters to move the
weight up 2 meters. Find the MA
GIVEN:
WORK:
MA = ?
De = 10 m
Dr = 2 m
MA = De ÷ Dr
MA= (10 m) ÷ (2 m)
MA= 5
DE
MA Dr
E. Efficiency (Honors)
 How well a machine works
 No machine is 100% efficient
 Many lose efficiency to friction,
or energy lost as heat
 Ex. If a machine is 90% efficient,
it means 10% of the energy is
lost as another form
E. Efficiency (Honors)
 Efficiency Formula:
Efficiency (%) Eff= Wout x 100
Win
 Efficiency equal the work out divided
by the work in multiplied by 100
 Output is always less than the input
work
Machines - Ch. 12
II. The Simple Machines

Lever
 Pulley
 Wheel & Axle

Inclined Plane
 Screw
 Wedge
A. Lever
 Lever
 a bar that is free to pivot about
a fixed point, or fulcrum
Resistance
arm
Effort arm
Fulcrum
Engraving from Mechanics Magazine, London, 1824
“Give me a place to stand and I will move the Earth.”
– Archimedes
A. Lever
 Ideal Mechanical Advantage (IMA)
 frictionless machine
Le
IMA 
Lr
 Le
Effort arm length
Resistance
arm length
must be greater than Lr in
order to multiply the force.
Problems
 You use a 160 cm plank to lift a large
rock. If the rock is 20 cm from the
fulcrum, what is the plank’s IMA?
GIVEN:
WORK:
Lr = 20 cm
Le = 140 cm
IMA = ?
Le
IMA = Le ÷ Lr
IMA = (140 cm) ÷ (20 cm)
IMA = 7
20cm
IMA
Lr
160cm
Problems
 You need to lift a 150 N box using only
15 N of force. How long does the lever
need to be if the resistance arm is 0.3m?
GIVEN:
WORK:
Fr = 150 N
Fe = 15 N
Lr = 0.3 m
Le = ?
MA = 10
Le = IMA · Lr
15N
Le = (10)(0.3)
Le = 3 m
Total length = Le + Lr
Total length = 3.3 m
0.3m
?
Le
IMA
150N
Lr
Le
IMA 
Lr
A. Lever
 First Class Lever
Fulcrum in the middle
 can increase force, distance, or
neither
 changes direction of force
 Examples: seesaws, scissors,
pliers

Le
IMA 
Lr
A. Lever
 Second Class Lever
 Output force in middle
 always increases force
 Example: wheelbarrows,
nutcrackers
Le
IMA 
Lr
A. Lever
 Third Class Levers
 Input force in middle
 always increases distance
 Examples: arms, legs,
baseball bats
Three Classes of Levers
B. Pulley
 Pulley
 grooved wheel with a rope or
chain running along the groove
 a “flexible first-class lever”
F
Le
Lr
B. Pulley
 Ideal Mechanical Advantage (IMA)


equal to the number of supporting
ropes on the load
You only count the end strand when
it is pointed up!
IMA = 0
IMA = 1
IMA = 2
What is the IMA?
=2
=3
=5
B. Pulley
 Fixed Pulley

IMA = 1 (so no
mechanical
advantage!)

does not
increase force

changes
direction of
force
B. Pulley
 Movable Pulley
IMA = 2
 increases force
 doesn’t change direction

B. Pulley Systems
 Block & Tackle



combination of fixed & movable pulleys
increases force (IMA = >1)
may or may not change direction
Pulley Systems
Pulley Systems
C. Wheel and Axle
 Wheel and Axle
 two wheels of different sizes
that rotate together
 a pair of
Wheel
“rotating
levers”
Axle
C. Wheel and Axle
 Ideal Mechanical Advantage (IMA)


effort force is usu.
applied to wheel
axle moves less
distance but with
greater force
re
IMA 
rr
effort radius
(wheel)
resistance radius
(axle)
Problems
 A crank on a pasta maker has a radius
of 20 cm. The turning shaft has a radius
of 5 cm. What is the IMA of this wheel
and axle?
GIVEN:
WORK:
re = 20 cm
rr = 5 cm
IMA = ?
IMA = re ÷ rr
IMA = (20 cm) ÷ (5 cm)
IMA = 4
re
IMA
5 cm 20 cm
rr
Problems
 A steering wheel requires a mechanical
advantage of 6. What radius does the
wheel need to have if the steering
column has a radius of 4 cm?
GIVEN:
WORK:
IMA = 6
re = ?
rr = 4 cm
re = IMA · rr
re = (6)(4 cm)
re = 24 cm
re
IMA
rr
rr
re
D. Inclined Plane
 Inclined Plane

sloping surface
used to raise
objects
l
IMA 
h
l
h
E. Screw
 Screw
 inclined plane wrapped in a
spiral around a cylinder
F. Wedge
 Wedge
 a moving inclined plane with 1
or 2 sloping sides
F. Wedge
 Zipper
2 lower wedges push teeth
together
 1 upper wedge pushes teeth apart

Problems
 How much force must be exerted to
push a 450 N box up a ramp that is 3 m
long and 1.2 m high?
Fl r
GIVEN:
WORK:
Fe = ?
Fr = 450 N
l=3m
h = 1.2 m
IMA = l ÷ h
IMA = (3 m)÷(1.2 m)
IMA = 2.5
Fe = Fr ÷ MA
Fe = (450 N)÷(2.5)
Fe = 180 N
MA
IMA F
he
Compound Machines
 A machine made up of more than
one simple machine
 Ex: car, pair of scissors, bicycles