2. In this section we will be looking at the mathematical
way for us to discover the Mechanical
Advantage, Speed Ratio, and Efficiency for
machines.
The formulas will be given to you in this
package…all you have to do is remember how to
apply them
3. Mechanical Advantage (MA)
This is the amount by which a machine is able to
multiply force.
The force that is applied to the machine is called
the input force
The amount of force the machine applies to the
object is called the output force
If you know the input and output forces you can
calculate the Mechanical Advantage
4.
5. Examples
It takes 45N to lift a 180N box with a pulley. What is
the MA?
It takes 75N to lift a 370N Crate with a ramp. What is
the MA?
It takes 24N to lift a 220N Beam with a double pulley.
What is the MA?
It take 220N to lift a 3215N Steel grate with a pulley.
What is the MA?
6. To SOLVE
1. It takes 45N to lift a 180N box with a pulley. What
is the MA?
45N = Input force
180N = Output Force
MA= output force = 180 = 4
input force 45
TRY THE REST!!
8. Speed Ratio (SR)
This is another way to analyze how machines work
Speed measures the distance an object travels in a
given amount of time
The measure of how the speed of an object is
affected by a machine is called the speed ratio
This is calculated by dividing the input distance by
the output distance
9.
10. A pulley System lifts a load 5m when two people pull
it 10m. What is the SR?
A pulley System lifts a load 6m when three people
pull it 24m. What is the SR?
A pulley System lifts a load 6m when one person
pulls it 16m. What is the SR?
A pulley System lifts a load 3m when five people pull
it 54m. What is the SR?
11. A pulley System lifts a load 5m when two people pull
it 10m. What is the SR?
SR = Input Distance = 10m = 2
Output Distance 5m
This means that the part of the system where you apply the
force is moving twice as fast as the place where the
output force is – where you are lifting the load
13. Less Force but Greater Distance
The calculations you have done so far do not give
you “something for nothing”
When using a pulley or ramp you must pull the rope
or push the object a greater distance than it actually
moves
Look at these two ramps. Find the Speed Ratio for
each 5m 10m
4m 4m
14. Mechanical Advantages Less than 1
Before we looked at MA values greater than one, but
there are a few machines that can cause a less than
1 Mechanical Advantage
For example; a Bicycle
A rider inputs 650N to the pedals but only results in
an output of 72. What is the MA? And what does this
mean?
15. Friction
The examples we have looked at are not completely
accurate because we have not included the effect of
friction into the equations
There will always be a difference between theoretical
and actual Mechanical Advantage because of friction
Friction is the force that opposes motion.
It is caused by roughness of a surface
The rougher the surface the more friction there is
16. Friction Continued
Because of friction extra force must be applied to
over come frictions effects
Mechanical advantage is affect by friction but speed
ratios is not, because speed ratios look at distance
rather than force being applied
Friction is important in another factor primarily when
it comes to heat.
Friction creates heat and heat can damage machines if
not contained
Special fans and lubricants are used to minimize heat
damage
17. Efficiency
Is a measurement of how well a machine or device
uses energy
When a machine operates it loses some sort of
energy in one way or another, primarily it is lost to
heat due to friction.
The more energy lost the less efficient the machine
is.
Efficiency is calculated as a percentage
A machine with 40% efficiency loses more energy than
one that is 70%
18. Pout = Mechanical Advantage
Pin = Speed Ratio
19. Examples
A Pulley has a SR of 6 and a MA of 3. What is its
efficiency?
A Pulley has a SR of 6 and a MA of 4. What is its
efficiency?
A Pulley has a SR of 15 and a MA of 4. What is its
efficiency?
A Pulley has a SR of 11 and a MA of 6. What is its
efficiency?
20. Solving
A Pulley has a SR of 3 and a MA of 2. What is its
efficiency?
Efficiency (%) = Mechanical Advantage x100 = 2 x100 =
66.67%
Speed Ratio 3
Solve the rest!
22. Complex Machines a Problem
In complex machines the many subsystems are
affected by friction and other factors
Because of this complex machines are often very
inefficient
A typical car engine has an efficiency of about 15%, which
means about 85% of the energy from gasoline is lost to heat
This is why over heating in car engines in a problem and
requires coolants and other technologies
