Pulley systems

Pulley systems. A pulley is a wheel with a grooved rim over which a string passes.

Types of pulleys.

(i) Single fixed pulley
(ii) Single movable pulley
(iii) Block and tackle pulley system

(i) Single fixed pulley

This is the type of pulley fixed on a rigid support.

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It is applied in:
Raising a flag
Lifting building materials during construction
Here, -load distance = effort distance
-tension is the same throughout the string.
-If no friction is considered, Load = Effort. Hence

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However, in practice the mechanical advantage and V.R of a single fixed pulley is less than one. Because of the following;
(i) Some energy is wasted in overcoming friction.
(ii) Some energy is wasted in lifting useless loads like threads.

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Here, the effort distance is twice the load distance.
Here, -load distance = 2 x effort distance
-tension is the same throughout the string.
-If no friction is considered, Load = Effort. Hence

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At balancing;
Sum of upward force = sum of downward forces

L=E+E

𝐋=𝟐𝐄

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M.A and V.R of a single movable pulley is two
However, in practice, the M.A. of a single movable pulley is less than two. Because of the following reasons;

(i) Some energy is wasted in overcoming friction.
(ii) Some energy is wasted in lifting useless loads like threads.

A single movable pulley is more advantageous than a single fixed pulley. In that, for a single movable pulley the effort required to raise a load is less that the load.

(ii) Block and tackle pulley system
This is consists of two blocks each having one or more pulleys, combined together to form a machine. This is done in order to have high velocity ratio and a higher mechanical advantage.
It is applied in:

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Note: (i) The number of portions of the string supporting the lower block is equal to the velocity ratio of the system.
(ii) The effort applied is equal to the tension in each string supporting the movable block.
E.g. If the effort is 6N, the tension in each string is also 6N.
(iii) For an odd number of pulleys in a system, the upper block contains one more pulley than the lower block. In addition, the string starts from the lower block.
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Passing the string
If the number of pulley wheels is odd, then the string should be tied down to the movable block.
For even number of pulley wheels, the string should be tied up to the fixed block.

Experiment to measure mechanical advantage and efficiency of pulley system.

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Determining effort: A known load is place on the load pan and knows weights are added to effort pan until the load just rises steadily when given a gentle push.

Repeating: The experiment is repeated with different loads and the results are recorded in table shown bellow:
V.R=……….

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Drawing the graph:
From the table a graph of efficiency or mechanical advantage against the load is plotted.

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Explanation of the shape of the graphs:
As the load increases, the efficiency also increases
This is because the weight of the movable pulley block and friction become very small compared to the load.

Note:
In practice, the movable block has some weight (w) and there is friction (F). These two together with the load (L) act downwards and they become part of the total downward forces.
Thus, the efficiency do not increase beyond 100% because;
i) some energy is wasted on overcoming friction
ii) Some energy is wasted on lifting useless loads like movable pulley blocks.

Therefore at Equilibrium;

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Example 1:
Below is a pulley system of mass 0.4kg, and there is friction of 5N

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(a) Calculate the;

(i) Velocity ratio of the system

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(b) If the load is raised through 6m, calculate the distance the effort moves at the same time.

Example 2:
Data

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Example 2:
A pulley system has two pulleys on the bottom block. A load of 1000N is hung from the bottom block, it is found that an effort of 300N to raise the load.
(i) How much energy is supplied, if the effort moves through 5m?

Solution
Data

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(iii)Find how much energy is gained by the load if the effort moves through 5m.

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Example 2:
A pulley system of velocity ratio 3 is used to lift a load of 100N. The effort needed is found to be 60N.
(a) Draw the arrangement of the pulley system.

Solution
Velocity ratio is odd. then;
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(b) Calculate the efficiency of the system.

Solution

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Coupled machines
If two or more machines are, coupled machines such that the output of one is connected to the input of the other, the over all performance is summed up by:
Overall -V.R = V.R1 + V.R2
-M.A. = M.A1 + M.A2
-Eff = Eff1 + Eff2

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The diagram above shows a pulley system used by a sailor for hoisting. Calculate the:
(a) Velocity ratio of the system

(a) Velocity ratio of the system

Solution
Velocity ratio of lower block = 4
Velocity ratio of middle = 2
Velocity ratio of upper block = 1
Overall V.R = 4 + 2+ 1 = 7

(b) The effort required to lift the load if the efficiency of the system is 75%.

solution

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Example:
The diagram below shows a screw jack being used to lift a car in order that a wheel may be charged.

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If the car bears down on the car with a force of 5000N and that efficiency of a screw jack is 15%. Calculate the;
a) V.R.

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NB: Work input is the work done by the effort. Sometimes it is considered as the work done by operator.

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From above, it is noted that work input is greater than workout put due to;
i) some work wasted in lifting useless loads,
ii) Some work wasted in reducing friction.

Note: For the screw the velocity ratio is very high because the length of the handle is very big compared to the pitch of the screw.

However the efficiency is very low. Usually lower than 50%. This is because friction is very high so the screw cannot run back if left.