unit d - section 2.1 --machines make work easier
DESCRIPTION
Section 2.1TRANSCRIPT
Machine Make Work Easier
Mr. Ilko
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
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
Mechanical Advantage
Output Force
Input Force
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?
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!!
SOLVE THE PROBLEMS
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
SR = Input Distance
Output Distance
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?
A pulley System lifts a load 5m when two people pull it 10m. What is the SR?
SR = Input Distance = 10m = 2Output 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
SOLVE
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
10m
5m4m 4m
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?
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
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
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%
Pout = Mechanical Advantage
Pin = Speed Ratio
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?
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!
2.
3.
4.
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