unit d - section 2.1 --machines make work easier

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Machine Make Work Easier Mr. Ilko

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Section 2.1

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Page 1: Unit d  - section 2.1 --machines make work easier

Machine Make Work Easier

Mr. Ilko

Page 2: Unit d  - section 2.1 --machines make work easier

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

Page 3: Unit d  - section 2.1 --machines make work easier

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

Page 4: Unit d  - section 2.1 --machines make work easier

Mechanical Advantage

Output Force

Input Force

Page 5: Unit d  - section 2.1 --machines make work easier

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?

Page 6: Unit d  - section 2.1 --machines make work easier

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!!

Page 7: Unit d  - section 2.1 --machines make work easier

SOLVE THE PROBLEMS

Page 8: Unit d  - section 2.1 --machines make work easier

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

Page 9: Unit d  - section 2.1 --machines make work easier

SR = Input Distance

Output Distance

Page 10: Unit d  - section 2.1 --machines make work easier

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?

Page 11: Unit d  - section 2.1 --machines make work easier

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

Page 12: Unit d  - section 2.1 --machines make work easier

SOLVE

Page 13: Unit d  - section 2.1 --machines make work easier

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

Page 14: Unit d  - section 2.1 --machines make work easier

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?

Page 15: Unit d  - section 2.1 --machines make work easier

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

Page 16: Unit d  - section 2.1 --machines make work easier

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

Page 17: Unit d  - section 2.1 --machines make work easier

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%

Page 18: Unit d  - section 2.1 --machines make work easier

Pout = Mechanical Advantage

Pin = Speed Ratio

Page 19: Unit d  - section 2.1 --machines make work easier

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?

Page 20: Unit d  - section 2.1 --machines make work easier

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!

Page 21: Unit d  - section 2.1 --machines make work easier

2.

3.

4.

Page 22: Unit d  - section 2.1 --machines make work easier

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