OBJ: What is a simple machine?
Simple Machines
 Defn: A machine consisting of only one part or
unit.
 6 simple machines in 2 categories
Levers
Inclined Planes
lever*
inclined planes*
pulley
wedge
wheel & axle
screw
 Simple machines can change:
1.the direction of force
2.the amount of force needed to do a job
3.the distance needed to move to do a job.
 THEY CANNOT REDUCE
THE AMOUNT OF WORK
NEEDED TO DO A JOB.
What is work?
 Work = Force x
 W =
F x
distance
d
W
F
d
 (Nm)
(N)
(m) units
 Work is measured in Nm
 A Newtonmeter is also known as a Joule (J)
Calculating Work
Example 1:
You lift a 700N dishwasher 1.5m off the ground to set it
on a truck bed. How much work did you do?
W= F x d
= 700N x 1.5m
= 1050 Nm or 1050 J
Without a simple machine there is
one force (your effort) and one
distance moved (your distance).
Fd
All You
YOU
Machine/Object
Fxd
Fxd
When you use a simple machine there are 2 forces & 2
distances used.
(You)
EFFORT (e is me)
 Fe - Effort Force
force you apply to the
machine
(object/ machine)
RESISTANCE
 Fr – Resistance Force
* force applied by the
machine to the object
(de) - Effort Distance
distance you must push
or pull
 dr - Resistance Distance
the distance the object
moves (by the machine)
 Work Input = Work
you do
 Work Output = work
the machine does
 Formula
Win= Fe x de
 Formula
Wout= Fr x dr
Lifting a box w/o a simple machine
Work = Force x distance
400
W = 400 N x 1 m
N
W = 400 Nm
1m
Lifting a box w/ a simple machine
Fe = 200 N
de = 2 m
Fr
Wout= Fr x dr
Win= Fe x de
Wout = 400 N x 1 m Win = 200 N
400 N
1m
dr
x2m
Wout = 400 Nm
Win = 400
Nm
 Note: Wout (Fr x dr) – is the work that would
be done w/o a simple machine or the work
done to the object you wish to move
 In an ideal machine
Win = Wout
Fe x de = Fr x dr
IN REALITY
Win > Wout Because of friction
OBJ: Discuss & Calculate Mechanical Advantage
Mechanical Advantage (MA)
The number of times a machine will
multiply your effort force
No units for MA
(multiplier)
Fe = 70 N
MA = ____
Fr = 210 N
Fe = ____ N
MA = 3
W = 270 N
 MA Formula
Fr
Actual MA = Fr ÷ Fe
MA Fe
 Example 1:
A claw hammer has an MA = 15 it is used
to pull a nail that exerts a resistance =
3000 N. How much force do you need to
pull with?
Fe = Fr / MA
= 3000 N ÷ 15
= 200 N
 Can you calculate MA using de & dr
instead?
Remember in an IDEAL MACHINE
that:
Win = Wout so…
Fe x d e = Fr x d r
Fe x d e = Fr x d r
Fe
Fe
d e = Fr x d r
Fe
d e = Fr x d r
dr
Fe x d r
de = Fr = MA
dr
Fe
 Alternate MA Calculation
de
MA dr
Theoretical MA = de/dr
Breakdown:
Fe – you
de – you
dr – object
Fr –Forces
objectin N
distances in m
MA - multiplier
 Example 2 – using the formulae together:
I set up a pulley system with a MA of 4 to lift
a 750 N crate. If I pulled 12 m of rope how
high did I raise the crate and how much force
did I need to apply (disregard friction)?
Fe =
Fr =
de =
dr =
MA =
What will a simple machine do if:
 MA = 1
(+) The machine may change the direction of a force
 MA > 1
(+) (Fe < Fr) The machine will multiply your effort force or makes the force easier for you
(-) (de > dr) makes your effort distance larger so you need to push/pull farther.
(+) The machine might change the direction of force.
 MA < 1
(-) (Fe > Fr) The machine makes is harder to push or pull.
(+) (de < dr) The effort distance is shorter so
you don’t have to push/pull as far.
(+) The machine may change the direction
of your force.
OBJ: Discuss levers, lever parts, lever classes, and MA of
levers.
 Lever Definition: a bar that is free to
pivot around a fixed point (fulcrum)
point where the
 3 parts to a lever
direction changes
Look for:
1. Fulcrum- the point where the lever
pivots or changes direction
Fe
2. Effort Arm- the section of the lever
where you will apply your effort force
(Fe)
Fr
3. Resistance Arm- the section of the
lever where the resistance (load) is
applied (Fr)
The bar is usually represented as a long
thin rectangle or line
 Data Points (measurements) on a lever
Fe
le
lr
Fr
le – length of the effort arm - distance
from the fulcrum to the point where
the effort force is applied
lr – length of the resistance arm distance from the fulcrum to the point
where the resistance or load is
We find: le/lr is proportional to de/dr so…
le
lr
=
de
dr
=
MA (Theoretical)
le
Theoretical MAlever =
le
lr
MA lr
3 Lever Classes
To identify the lever class ask “What’s in
the middle?” The answer is 1-2-3 F-R-E
1st Class Lever
Fulcrum in the middle*
ex: see saw, balance,
oar,
2nd Class Lever
middle*
Resistance is in the
ex: wheelbarrow,
3rd Class Lever
Effort is in the middle*
ex.: tennis racquet,
* middle just means between the other two
1st Class Levers could have
MA = 1,
lr
MA > 1,
lr
MA < 1
le
lr
le
with the fulcrum ½ way between the
effort & resistance lr = le so MA = 1
Advantage: changes direction of force
with the fulcrum closer to the
resistance lr < le so MA > 1
Advantages: Easier Effort & changes
direction of force
le
with the fulcrum closer to the effort
lr > le so MA < 1
Advantages: Shorter distance &
changes direction of force
2nd Class Levers have MA > 1
lr
le
lr < le so MA > 1
Advantage: Easier Effort
3rd Class levers have MA < 1
lr
le
lr > le so MA < 1
Advantage: Shorter Effort distance
Example 2: A certain lever has a resistance arm of 2 m. You are trying to lift a 1500
N box with this lever and you can apply a maximum force of 800 N. How long does
the lever need to be and what is its MA?
1)
2)
3)
List everything you know/need & draw a picture.
Then solve for the missing value using one of the above methods.
Then answer the questions.
Fr =
Fe= 800 N
Fe =
lr =
Fr = 1500 N
le =
le= ?
lr = 2 m
OBJ: Discuss Pulley Systems & their mechanical
advantage
Pulleys
 Defn: A simple machine with a grooved wheel
that rotates on a shaft or axle
 Most pulley systems can have up to 2
advantages
1.MA > 1 so Fe < Fr - Multiplies your effort
force (reduces the effort you need to pull
with)
2.Might change the direction of your force
SINGLE FIXED PULLEY SYSTEM
 Pulley is anchored to an object
 Only benefit is that it changes
direction of your force.
 Effort & resistance arms are equal
 MA = 1
 Does not multiply force
Fe
Fr
 A Single Fixed Pulley has 2 “strings” but only
one supporting string
SINGLE MOVEABLE PULLEY SYSTEM
 the string or rope is anchored and
the weight (Fr) hangs off the
pulley so the pulley moves
Fe
 Fe < Fr
 de > dr
 MA = 2
Fr
(+) effort force is easier
(-) effort distance is longer
 A Single Moveable Pulley has 2 “strings” and
both are supporting strings
Support Strings
 The number of “sections” of the string that support
or hold up the weight
o Each time the string passes around a pulley it
counts as a new string “section”
o Only those “sections” that support the weight in
an upward direction are considered support
strings.
 If your EFFORT STRING (section you are
pulling) is pulling DOWN, DON’T COUNT IT as
a support string.
 If your EFFORT STRING (section you are
pulling) is pulling UP, COUNT IT as a support
string
MULTIPLE PULLEY SYSTEMS
A combination of fixed & movable pulleys
used to lift heavy objects (a.k.a. Block &
Tackle)
MA > 1
MA = # of support strings
How to Draw Multiple Pulley Systems
1. Draw the anchor (top)
2. Draw the Pulley Frames
(one anchored, one floating)
3. Draw the Resistance (Fr)
on the bottom of the lower
pulley frame
4. a. Start the string with the
effort in the direction you
want to pull
b. Working backwards
(outside to inside) loop the
string around the anchors
until you get the MA you
need
c. Attach the string to the
next pulley frame.
5. Draw the wheels
Fr
Obj: Discuss the Wheel & Axle
Wheel & Axle:
 A simple machine that consists of a
larger “wheel” fixed to a smaller “wheel”
or shaft called the axle
 There is no slip between the wheel & the
axle so they both turn together
Wheel
Axle
 Examples:
Doorknob, steering wheel, pencil sharpener,
bike crank, can opener, faucet handle,
wrench…
Fe
Fr
 MA of a Wheel & Axle
o If you apply your effort (Fe) to the
wheel, the MA > 1
(Fe < Fr & de > dr)
 Examples:
Fishing reel, pencil sharpener, steering wheel
Fr
o If you apply your effort (Fe) to the
axle, the MA < 1
( Fe > Fr & d e < d r )
 Examples:
Rear wheel on a bike, fan…
Fe
 A wheel & axle cannot change the
direction of a force.
How do you increase the MA of a screwdriver?
Obj: Discuss inclined planes
Inclined Planes
 Defn: a ramp or slanted surface used to
raise or lift objects
 Examples:
o Ramp, half-pipe, stairs, roof, ladder,
hill
 Remember theoretical MA for a SM
de
l
h
In an I.P.
MA dr
de = l
dr = h
 Mechanical Advantage (MA) of an
Inclined Plane
o Theoretical MA =
(Ideal I.P.)
length or l
height or h
l
MA h
o MA > 1 (multiplies Fe) because length >
height
 Since Win = Fe x de = Fe x length and
Wout = Fr x dr = Fr x height
 Remember Fe is your force & Fr is the objects weight
Obj: Discuss wedges, screws, & power
Wedge:
 Defn: 2 inclined planes put together
 Usually used to separate objects
 Examples: axe, knife, doorstop, shims, splitting
wedge, nail
 Low efficiency
Screw:
 Defn: an inclined plane wrapped around a cylinder
Fine Threads
Coarse Threads










shallow slope
more tpi (threads/inch)
higher MA
easier to turn
pulls in slower
steeper slope
fewer tpi
lower MA
harder to turn
pulls in faster
Power:
 The rate of doing work
 Formula:
Power = Work or P = W or P = F x d
Time
t
t
W
P t
 Units:
o Power is measured in Watts (W)
o 1 Watt = 1 Nm/s or 1 J/s
o 1000 Watts = 1 kiloWatt (kW)
Sample Power Problem: It takes 35 seconds to raise
an 870 N man 1 m in the air using the pulley
system. Calculate the power generated.
Example:
Calculate the theoretical MA of the ramp and
the Fe needed to push a 1200 N barrel up a 10 m
inclined plane with a height of 2 m
l =10 m
h=2 m
Fe
Fr =
1200 N
Fr =
l
l=
MA h
h=
Fr
MA =
MA Fe
Fe =
Obj: Discuss & Calculate Efficiency
Remember:
 Due to friction we have less than the ideal
machine so Win > Wout
Fr
 Actual MA is calculated w/ forces
MA Fe
Efficiency
 Defn: the ratio of Win to Wout
 Formula:
% Efficiency =
Wout x 100 so…
Win
% Efficiency =
Fr x h x 100
Fe x l
 Tells you what % of YOUR force (Fe) actually
goes to doing the job. The remainder (out of
100%) is used to fight friction.
o High Efficiency (example 80%)
 Most of your work is useful &
used to do the job.
 80% used to do the job
 20% used to fight friction (lost, wasted)
 (levers, good pulleys & good wheel & axles)
o Low Efficiency (example 40%)
 Most of your work is lost or wasted to
friction
 40% is used for the job
 60% is lost to fight friction
 inclined planes, screws, wedges, poor pulleys &
wheel & axles
 How can you improve efficiency?
Answer: Reduce Friction
o For an Inclined Plane (I.P.)
 Make the surface smoother (sanding,
waxing, etc.)
 Put the object on wheels
 Lubricate the wheels or surface
Sample Efficiency Problem: We designed a
pulley system with an MA of 4 to lift a person
(870 N). I was able to lift that person 1 m by
exerting a force of 315 N. Find how much rope
I had to pull and the efficiency of the system.
Fe =
Fr =
de =
dr =
MA =
% Efficiency = Fr x h x 100
Fe x l