We all know what a wheel is, but what’s a pulley?  Pulley is a wheel used to change the magnitude or the direction of a pull using a rope. Pulleys can be named as we use them, fixed or movable. When a lot of pulleys are used for a single rope, it becomes a pulley system. Wheels are normally used to reduce friction,. But the rubber tyres increase friction for a better grip of the road. Here we consider wheels used as machines only, that is those that change the magnitude or direction of a  force. 

Fig.1. A pulley system.

There are 3 pulleys in this system each weighing 2 N. The blue pulleys can move up and down while the green is fixed. As the 30 N load is suspended by two strands, each strand will get only half the load. What is the effort required by Tommy?

Fig. 2  .gives an interesting experiment with a fixed pulley. Two plastic cups are hanging from either side of the pulley. Consider one as the LOAD then the other becomes EFFORT required to raise it. To measure the force, we  can use marbles, coins, nails or some other such material. (The pulley has to be very light and well oiled to reduce friction.)
We already know that this kind of a pulley can change the direction of a force. Now we should try to find out whether  it can change the magnitude (size) of a force. Can the three marbles be lifted by a lesser number of marbles?  You can record the results in a table similar to the one given below.

 

Fig.2. An experiment with a fixed pulley. 

LOAD		EFFORT
Magnitude	Distance moved	Magnitude	Distance moved
1 unit	10 cm
2 units	10 cm
3 units	10 cm

 If you have done the experiment correctly you will find the distance moved by load and effort are always the same. What about the magnitudes? Can you lift three marbles by using less than that?
So the conclusion of many is that a fixed pulley does not give an advantage except for the changing of the direction.

 

Fig.3. Using a pulley as a movable one.

 Another way to use a pulley is to attach the pulley to the load. Then the pulley travels up and down with the load. You might think that this is not a good method, as you have to lift the pulley also. In Fig.4 the box weighs 20N. What do you think the weight the hand gets? Is it 20 N, or more or less?  If you have a spring balance you can straight away find out the foce the hand has to give. Or else you can do this experiment to get a good understanding of using a movable  pulley.

 

Fig.4  A pulley system.

 Here in addition to the movable pulley , we are using a fixed pulley.  This way we can use weights on the pans provided .  L marked one is the Load while the E marked one is the Effort.  You can find out for yourself the effort required to lift different loads. Record your results using a table as for the previous experiment.

 Velocity Ratio and Mechanical Advantage.

 These are two important ratios which are very useful for the study of simple machines such as pulleys.

 

Velocity Ratio gives a number equivalent to show how many times the Effort moves more than the load during a certain time. The formula is ;

Velocity Ratio =    Displacement of Effort  /    Displacement of Load.

 Mechanical advantage gives the number of time the load can be heavier than the effort. The formula  is;

Mechanical advantage =   Load / Effort.

Worked out Example 

 

Fig. 6 Mechanics of a movable pulley. 

•  A load of 10 N is raised using a pulley weighing 2N as shown in Fig.6. Neglecting friction and the weight of thread, find the following:

 

          1.    Velocity Ratio.   2.  Effort required     3. Mechanical advantage.

          1.  Using the formula V.R  =   Displacement of Effort / Disp. of Load

                                                         =    2/1      =   2.
          2. Load and the pulley weighs    =   10 + 2  N

                                                                    =   12 N

             The load is supported by two strands of thread.

             Therefore each thread will get a force  =  12/2  =   6N

           3.  Mechanical advantage  =  Load / Effort

                                                           =   10/  6 N

                                                           =  1.7
 

 Further Activity
It will be an interesting exercise to find out how the Mechanical advantage changes according to the Load.   Use this chart for the purpose.
 

Useful Load	10 N	20 N	30 N	40 N	50 N	60 N	70 N
Load + Pulley= Final Load	10 + 2  N   12 N	20 + 2 N   22 N
Effort	6 N	11 N
Mechanical advantage	10/6 = 1.7	20 /11 = 1.8

 

 What do you think is the highest possible Mechanical advantage?

Efficiency

Efficiency is another important ratio regarding machines. It gives the ratio of actual energy required to do some work is to the  total energy that has to be used. This is usually given as a percentage.   Here area few Formulae which may be used to find the Percentage efficiency of a machine.

 Percentage Efficiency =   Work output / Work input  X 100

 Percentage Efficiency =  Mechanical Advantage / Velocity Ratio

 Percentage Efficiency + Energy loss = 100

  Extension 1. on Pulleys.

                      Wheel and axle

In a double pulley the two wheels can turn independently. In this system the two pulleys are fused together. When the large wheel goes one round the axle will also turn one round. If you take the distance effort moves as the circumference of the large circle, the distance moved by the load will be the circumference of the axle.

 

 Velocity ratio of machine  = 

Circumference of the large circle /  The circumference of axle.    
                     Velocity ratio   =     2 π  x  r_w /  2 π x r_a
                                                =  r_w  /  r_a
 

 Extension 2. on Pulleys.

                          Belt drive

 

Fig.  A belt driven motor cycle.

A motor car has two vital belt drives.  One sets the timing for the pistons to work by connecting the crank shaft with the cam shaft. The other drives the Alternator ,  air conditioning compressor, power steering pump, cooling fan, and air injection pump,.

In a normal pulley system, the magnitude of the force is changed by the distances, the rope moves. The pulleys are there to reduce friction while changing the direction. In a belt drive, the belt moves at a constant speed while the pulleys or rollers rotate at different speeds depending on their radii .  

Here is an analysis of a system.

 

	Blue pulley	Green pulley
Radius	5 cm.	10 cm.
Circumference	2 π x rb	2 π x rg
Rotating speed	1000 revolutions per minute.	…………………………….rpm
Distance tape moves / min	1000 x 2 π x 5	Same 1000 x 2 π x 5

 

Will the green pulley rotate at the same speed,  ?

Silly says  “same”.   Ali says “Slow”  Billy says “ fast”    Who is right?

 

Rotating speed

1000 rpm

1000 x 2 π x 5 /  2 π x rg = 1000 x 5  /  10 = 5000/ 10  =  500 rpm

 

Large wheel turns slowly.  

 

 Extension 3

                                  COG WHEELS or GEARS

 Cog wheels can work in two major ways; touching each other as in Fig. or if apart, with a chain drive.  If the black wheel turns  clockwise, which way will the brown wheel rotate?
That’s easy. OK   Now answer this.  If the black one rotates at 45 rpm what will be the speed of the brown wheel?

Method  1
No of black teeth that will pass in a minute =  16 x 45
No of brown teeth that will pass in a minute= 16 x 45   (No of teeth passing has to be the same.)
8 Brown teeth passes for one revolution
For . 16 x 45 teeth to pass no. of rev.  =      16 x 45  /   8
                                                             = 90 revolutions.

Method   2

Method 2
The ratio of black teeth: Brown teeth = 16 : 8
                 This is                                = 2 : 1
Brown will turn twice as fast the other
                                                           = 45  x 2  = 90 rpm.

 

 
1.0    Pineapple is attached to a pulley and hanging from a force measurer. It reads 15 N. The pulley has a weight of  2N.  

Find the following:-
1.1  velocity ratio,                                   1.2  mass of the pineapple?                   1.3 mechanical advantage?
1.4  Efficiency percentage                      (20 marks) marks)                                                                                               

2.0   If a machine has an efficiency of  80% and a velocity ratio of 2  how much will be the effort required for a load of  700 N?                                                                                    (10 marks)
3.0  The man is lifting a log weighing 1200 N using a pulley system. Each pulley weighs 5 N

3.1  if the man pulls 20 m of rope  find the displacement of the log and thereby the velocity ratio.
3.2  Neglecting friction, find the minimum effort required for the man to raise the load..
3.3 Neglecting friction but considering the weight of pulley,  find the efficiency of the system.
3.4 If the efficiency is taken into consideration will the efficiency be higher or lower ?
3.5    If you use a much lighter load , will the efficiency be higher or lower?                         

(20 marks)     
4.0

 

Two sets of smooth  double pulleys have been used in two different ways  Set A and set B.  Copy this table and write the answers to these. One set of double pulleys weighs  18 N.  The load is 482 for both

Question	A	B
4.1  How many strands are supporting the load?
4.2  What is the velocity ratio?
4.3  What will be the effort required to lift a load of 482.0?
4.4 What is the mechanical advantage?
4.5 What is the percentage efficiency?

( 20 marks.)

 

5.0

 

The data sheet,     
Diameter of wheel 36 cm
Diameter of axle    6 cm.
Find the effort required to raise a load of 750 N neglecting friction.                        (10 marks)

6.0 

(10 marks)

7.0

 

1    When the pedal does one round how many rounds will the bicycle tyre will go?
2    If the length of the pedal is 25 cm and the radius of the rare wheel is 40 cm find the distance the bike will go for one turn of the pedal.                                                                         (10 marks)

For solutions visit Answer page.