machinesmachines machines machines force work power mechanical advantage ideal machines 6...
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Machines Machines Machines Machines Machines
Machines Force Work Power Mechanical Advantage Ideal Machines 6 Simple Machines Efficiency
Machines
Machinedevice that makes work easierchanges the size and/or
direction of the exerted force
Work
A force causes an object to moveThe movement must be in the
same direction as the applied force.
Units: Nm or Joules (J)
W = F × d
Powerrate at which work is donemeasured in watts (W)
P = W
t P = power (W)
W = work (J)
t = time (s)
Calculating Power
P = W ÷ t
W = F·d
W = (450 N)(1.5 m) = 675 J
P = 675 J ÷ 3.0 s
P = 225 W
F = 450 N
d = 1.5 m
t = 3.0 s
A figure skater lifts his partner, who weighs 450 N, 1.0 m in 3.0 s. How much power is required?
Forces
Effort Force (Fe)force applied to the machine“what you do”
Resistance Force (Fr)force applied by the machine“what the machine does”
WorkWork Input (Win)
work done on a machine
Work Output (Wout)
work done by a machine
Win = Fe × de
Wout = Fr × dr
Ideal Machine EquationConservation of Energy
can never get more work out than you put in
trade-off between force and distance
Win = Wout
Fe × de = Fr × dr
Ideal Machine Equation 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?
0.3m
Fe × de = Fr × dr
(15 N) de = (150 N)(0.3m)
de = (150 N)(0.3m)
15N
de = 3.0 m
Work In an ideal machine...
But in the real world…some energy is lost as friction
Win = Wout
Win > Wout
Mechanical AdvantageMechanical Advantage (MA)
number of times a machine increases the effort force
e
r
F
FMA
MA > 1 : force is increasedMA < 1 : distance is increasedMA = 1 : only direction is changed
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:
Fe = 20 N
Fr = 500 N
MA = ?
WORK:
MA = Fr ÷ Fe
MA = (500 N) ÷ (20 N)
MA = 25
MA
Fr
Fe
Mechanical Advantage Find the effort force needed to lift a
2000 N rock using a jack with a mechanical advantage of 10.
GIVEN:
Fe = ?
Fr = 2000 N
MA = 10
WORK:
Fe = Fr ÷ MA
Fe = (2000 N) ÷ (10)
Fe = 200 N
MA
Fr
Fe
Efficiencya measure of how completely work input is converted to work output
100%W
WEfficiency
in
out
always less than 100% due to friction
Lever
A lever is a bar that is free to pivot about a fixed point, or fulcrum.
“Give me a place to stand and I will move the Earth.”– Archimedes
Engraving from Mechanics Magazine, London, 1824
Resistancearm
Effort arm
Fulcrum
Mechanical Advantage
r
e
L
LIMA
Ideal Mechanical Advantage (IMA) frictionless machine
Effort arm length
Resistancearm length
Le must be greater than Lr in order to multiply the force.
First Class Lever
a. can increase force, distance, or neither
b. changes direction of force
r
e
L
LIMA
Second Class Lever
r
e
L
LIMA
always increases force
Third Class Leverr
e
L
LIMA
always increases distance
Pulley
a. a grooved wheel with a rope or chain running along the groove
b. a “flexible first-class lever”
Le
Lr
IMA of a Pulley
equal to the number of supporting ropes
IMA = 0 IMA = 1 IMA = 2
Single Fixed PulleyIMA = 1
does not increase force
changes direction of force
Block and Tackle
combination of fixed & movable pulleys increases force (IMA = 4) may or may not change direction
Wheel and Axle
a. two wheels of different sizes that rotate together
b. a pair of “rotating levers”
IMA = radius of wheel radius of axle
IMA Problems 1. 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?
IMA = Le
Lr
IMA = (140 cm) ÷ (20 cm)
IMA = 7
IMA = ?
Lr = 20 cm
Le = 140 cm
2. 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?
IMA = ?
rw = 20 cm
ra = 5 cm
IMA = rw ÷ ra
IMA = (20 cm) ÷ (5 cm)
IMA = 4
3. 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?
rw = IMA · ra
rw = (6)(4 cm)
rw = 24 cm
ra
rw
IMA = 6
rw = ?
ra = 4 cm
Inclined Plane
h
lIMA
sloping surface used to raise objects
Inclined Plane 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?
IMA = l ÷ hIMA = (3 m)÷(1.2 m)IMA = 2.5
Fe = Fr ÷ MAFe = (450 N)÷(2.5)Fe = 180 N
Fe = ?
Fr = 450 N
l = 3 m
h = 1.2 m
A worker exerts a force of 500 N to push a 1500 N sofa 4.0 m along a ramp that is 1.0 m high. What is the ramp’s efficiency?
Fe = 500 N
de = 4.0 m
Fr = 1500 N
dr = 1.0 m
Win = (500N)(4.0m) = 2000 J
Wout = (1500N)(1.0m) = 1500 J
E = 1500 J × 100% 2000 J
E = 75%4.0m4.0m
1.0m
500N
1500N
100%in
out
W
WE
Screw
inclined plane wrapped in a spiral around a cylinder
Wedgea moving inclined plane with 1 or 2 sloping sides
Rube Goldberg Machine
Rube Goldberg walks in his sleep, strolls through a cactus field in his bare feet, and screams out an idea for self-operating napkin: As you raise spoon of soup (A) to your mouth it pulls string (B), thereby jerking ladle (C) which throws cracker (D) past parrot (E). Parrot jumps after cracker and perch (F) tilts, upsetting seeds (G) into pail (H). Extra weight in pail pulls cord (I), which opens and lights automatic cigar lighter (J), setting off sky-rocket (K) which causes sickle (L) to cut string (M) and allow pendulum with attached napkin to swing back and forth thereby wiping off your chin. After the meal, substitute a harmonica for the napkin and you'll be able to entertain the guests with a little music.