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What is Work?Work
transfer of energy that occurs when a force makes an object move
W = FdW: work (J)F: force (N)d: distance (m)
1 J = 1 N·m
Distance must be in direction of force!
FWd
Doing Work If you push on your desk and
nothing moves, have you done work?No
Conditions for work to be done:Force must make object moveThe movement must be in the
same direction as the applied force.
Work and EnergyWhen work is done, a transfer
of energy always occurs. If you carry a heavy box up a
flight of stairs, you transfer energy form your moving muscles to the box (increasing its PE by increasing its height).
Lifting ProblemBrett’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
FWd
Dancing is WorkA 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?
GIVEN:
m = 40 kg
d = 1.4 m - during
d = 2.2 m - after
W = ?
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. F
Wd
Power in Skating A figure skater lifts his partner, who
weighs 450 N, 1.5 m in 3.0 s. How much power is required?
GIVEN:
F = 450 N
d = 1.5 m
t = 3.0 s
WORK:
P = W ÷ t
W = F·d
W = (450 N)(1.5 m) = 675 J
P = 675 J ÷ 3.0 s
P = 225 W
P
W
t
Self Check 5.11. The amount of work done
depends on what two things?
2. You push a box with a force of 100 N. If it moves 5 m while you are pushing, how much work was done?
What is a Machine?
Machinedevice that makes work easierchanges the size and/or
direction of the exerted force
Making Work Easier Machines make work easier by:
increasing the force that can be applied to an object
car jack increasing the distance over which
a force can be applied ramp
changing the direction of an applied forcewedge-shaped blade of ax
Input and Output Forces
Input Force (Fin)force applied to the machine“what you do”
Output Force (Fout)force applied by the machine“what the machine does”
Force and WorkWork Input (Win)
work done on a machine
Work Output (Wout)
work done by a machine
Win = Fin × din
Wout = Fout × dout
Conserving EnergyConservation of Energy
can never get more work out than you put in
trade-off between force and distance
Win = Wout
Fin × din = Fout × dout
Ideal Machines 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 input force
€
MA =FoutFin
MA > 1 : force is increasedMA < 1 : distance is increasedMA = 1 : only direction is changed
Open a Window A worker applies an input force of 20 N
to open a window with a output force of 500 N. What is the crowbar’s MA?
GIVEN:
Fin = 20 N
Fout = 500 N
MA = ?
WORK:
MA = Fout ÷ Fin
MA = (500 N) ÷ (20 N)
MA = 25
MA
Fout
Fin
Mechanical Advantage Find the input force needed to lift a
2000 N rock using a jack with a mechanical advantage of 10.
GIVEN:
Fin = ?
Fout = 2000 N
MA = 10
WORK:
Fin = Fout ÷ MA
Fin = (2000 N) ÷ (10)
Fin = 200 N
MA
Fout
Fin
Mechanical AdvantageWindow blinds change direction
of the input force.The input and output forces
are equal, so the MA = 1
EfficiencyEfficiency
measure of how completely work input is converted to work output
100%W
WEfficiency
in
out
In real machines, it is always less than 100% due to friction
Ramps 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?
GIVEN:
Fin = 500 N
din = 4.0 m
Fout = 1500 N
dout = 1.0 m
WORK:
Win = (500N)(4.0m) = 2000 J
Wout = (1500N)(1.0m) = 1500 J
E = 1500 J × 100% 2000 J
E = 75%
1.0m
1500N
4.0m500N
100%in
out
W
WE
Increasing EfficiencyMachines can be made more
efficient by reducing friction. A lubricant fills in the gaps
between surfaces, enabling them to slide past each other more easily.
Self Check 5.2Why is the work output always
less than the input in a real machine?
Calculate the mechanical advantage of a hammer if the input force is 125 N and the output force is 2000 N.
Simple MachinesA simple machine is a machine
that does work with only one movement of the machine.
There are six types of simple machines: levers, pulleys, wheel and
axle, inclined planes, screws, and wedges.
LeversLever
a bar that is free to pivot or turn around a fixed point
The fixed point the lever pivots on is called a fulcrum
Types of LeversFirst class lever
fulcrum in middle
Second class leverFout in middle
Third class leverFin in middle
PulleysPulley
grooved wheel with a rope or chain running along the groove
a “flexible first-class lever”axel of pulley is the fulcrum
Lin Lout
F
IMA of a Pulley Ideal Mechanical Advantage (IMA)
equal to the number of supporting ropes
IMA = 0 IMA = 1 IMA = 2
Comparing PulleysFor a fixed pulley, the distance
you pull the rope downward equals the distance the weight moves upward.
For a movable pulley, the distance you pull the rope upward is twice the distance the weight moves upward.
Block and Tackle PulleysBlock & Tackle
combination of fixed & movable pulleys
may or may not change direction
IMA = 4
Wheel and AxleWheel and Axle
two wheels of different sizes that rotate together
a pair of “rotatinglevers”
Wheel
Axle
Wheel and Axle Is this skateboard a good
example of a wheel and axel machine?No because
the axle is fixed.
IMA Wheel and Axle Ideal Mechanical Advantage (IMA)
effort force is applied applied to at rim of wheel
axle moves less distance but with greater force
r
e
r
rIMA
effort radius
resistance radius
ScrewScrew
inclined plane wrapped in a spiral around a cylinderinput force by turning screwoutput force on threads
A. Compound MachinesRube 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.
Videos http://www.brainpop.com/technology/simplemachines/
levers/ http://www.brainpop.com/technology/simplemachines/
pulley/ http://www.brainpop.com/technology/simplemachines/
wheelandaxle/ http://www.brainpop.com/technology/simplemachines/
inclinedplane/ http://computerkiddoswiki.pbworks.com/Simple-Machines http://www.edheads.org/activities/odd_machine/
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:
Lr = 20 cm
Le = 140 cm
IMA = ?
WORK:
IMA = Le ÷ Lr
IMA = (140 cm) ÷ (20 cm)
IMA = 7
IMA
Le
Lr
20cm
160cm
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:
re = 20 cm
rr = 5 cm
IMA = ?
WORK:
IMA = re ÷ rr
IMA = (20 cm) ÷ (5 cm)
IMA = 4
IMA
re
rr
5 cm 20 cm
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:
IMA = 6
re = ?
rr = 4 cm
WORK:
re = IMA · rr
re = (6)(4 cm)
re = 24 cm
IMA
re
rr
rr re
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:
Fr = 150 N
Fe = 15 N
Lr = 0.3 m
Le = ?
MA = 10
WORK:
Le = IMA · Lr
Le = (10)(0.3)
Le = 3 m
Total length = Le + Lr
Total length = 3.3 m IMA
Le
Lr
0.3m
?
150N
15N
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?
GIVEN:
Fe = ?
Fr = 450 N
l = 3 m
h = 1.2 m
WORK:IMA = l ÷ hIMA = (3 m)÷(1.2 m)IMA = 2.5
IMA
l
hMA
Fr
Fe
Fe = Fr ÷ MAFe = (450 N)÷(2.5)Fe = 180 N