Mechanical Advantage

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Mechanical Advantage
What do simple machines do for us
anyway?
There are four ways that a
machine helps us to do work.




Transfers our effort force from one
place to another. Ex: seesaw
Multiply your effort force.
Ex: crowbar
Magnify speed and distance.
Ex: baseball bat
Changing the direction of the force.
Ex: pulley on the flagpole
There are 2 types of mechanical
advantage.




IMA – Ideal
mechanical
advantage.
This is the number of
times a machine is
designed to multiply
your effort force.
It is based on
measurements of the
machine.
Ignores friction




AMA – Actual
mechanical advantage
This is the number of
times the machine
actually multiplies
your effort force.
AMA = resistance
force/effort force.
Includes the effects of
friction
IMA is always larger than AMA.
Mechanical Advantage


Definition
- a quantity that measures how much a
machine multiplies force or distance
Two types
 Actual: measures the actual forces action
on a machine
- AMA = output force
input force
 Ideal: measures the mechanical
advantage in the absence of friction
- IMA = input distance
output distance
Mechanical Advantage Problems
Q: Alex pulls on the handle of a claw hammer
with a force of 15 N. If the hammer has a
actual mechanical advantage of 5.2, how
much force is exerted on a nail in the claw?
A: output force = (5.2)(15N) = 78 N
Q: If you exert 100 N on a jack to lift a
10,000 N car, what would be the jack’s
actual mechanical advantage (AMA)
A: AMA= 10,000 N / 100 N = 100
Mechanical Advantage Problems
Q: Calculate the ideal mechanical advantage
(IMA) of a ramp that is 6.0 m long and 1.5
m high?
A: IMA = 6.0m / 1.5m = 4.0
Q: The IMA of a simple machine is 2.5. If the
output distance of the machine is 1.0 m,
what is the input distance?
A: Input distance = (2.5)(1.0m) = 2.5 m
Efficiency of Machines


Definition
- a quantity, usually expressed as a
percentage, that measures the ratio of
useful work input
Formula
- Efficiency = useful work output
work input
- % of work input that becomes work
output
- due to friction, efficiency of any machine
is always less than 100%
Efficiency Problems
Q: Alice and Jim calculate that they must do 1800 J of
work to push a piano up a ramp. However, because
they must also overcome friction, they must actually
do 2400 J of work. What is the efficiency of the
ramp?
A: 1800 J/ 2400 J x 100 = 75%
Q: If the machine has an efficiency of 40%, and you do
1000 J of work on the machine, what will be the
work output of the machine?
A: Work Output = (Efficiency x work input) / 100%
Work Output = (40% x 1000 J) / 100% = 4.0 x
102 J
Simple Machines


Definition
- one of the six basic types of
machines
2 types or families
1. lever
2. inclined planes
Levers

-
Definition
- a rigid bar that is free to move around a
fixed point
ex. screwdriver
all levers have a rigid arm that turns
around a point called the fulcrum
force is transferred from one part of the
arm to another
original input force can be multiplied or
redirected into output force
levers are divided into 3 classes, based on
the locations of the input force, output
force, and the fulcrum
There are 3 Classes of Levers

Depends on the location
of 3 items:
1. Fulcrum – fixed point
on a lever
2. Effort Arm – the part
of the lever that
exerts the effort force.
3. Resistance Arm – the
part of the lever that
exerts the resistance
force.
 EA

RA
1st Class Lever




Changes the
direction of the
force
Multiplies effort
force
Magnifies speed
and distance
Ex: seesaw,
crowbar, scissors
2nd Class Lever



Multiply effort
force
Mechanical
advantage is
always greater
than 1.
Ex: bottle opener,
boat oars, wheel
barrow
3rd Class Lever



Magnifies speed
and distance
Mechanical
Advantage always
less than 1
Ex: baseball bat,
golf club, broom,
shovel
Wheel and Axis

-
-
Definition
- simple machine that consists of two
disks or cylinders, each one with a
different radius
ex. steering wheel, screwdriver
made of a level or a pulley (wheel)
connected to a shaft (axle)
small input force, multiplied to become
a large output force
Inclined Planes

-
Definition
- slanted surface along which a force moves an
object to a different elevation
ex. knife, ax, zipper, wedge, screw
ramp redirects the force applied to lift object
upward
turns a small input force into a large output
force by spreading the work out over a large
distance
- wedge: functions as two inclined planes back
to back, turning a downward force into two
forces
directed out to the sides
-screw: an inclined plane wrapped around a
cylinder
Pulleys

Definition
- a simple machine that consists of a rope that fits
into a groove in a wheel.
- very similar to a lever
-

point in the middle of the pulley is like a fulcrum
rest of the pulley acts like the rigid arm
3 Types of Pulleys
- fixed pulleys
- moveable pulleys
- pulley system
Fixed And Movable
Pulley System
1. What is the IMA of
this pulley system?
2. Ignoring friction, if
you want to lift the
resistance 3 meters
what will the effort
distance be?
3. Ignoring friction
how much effort force
will be necessary to
lift a load of 15
newtons?
4. How much work is
done?
Compound Machines

Definition
- a machine that is made of
more than one simple machine
ex. scissors, jacks, bicycle,
washing machine,
car, clock
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