Question

A pulley system with a velocity ratio = 4 is used to lift a load of 300 kgf to a vertical height of 10 m by applying an effort of 100 kgf downwards.

Calculate:
(i) Efficiency of the pulley
system and,

(ii) Work done by the Effort.
__________

Answer please
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Answer 1

$\large\text{Given:}$

$\rightarrowtail \bold{Velocity\;ratio\;=4}$

$\rightarrowtail \bold{Load\;=\;300kgf}$

$\rightarrowtail \bold{Displacement\;of\;load\;=\;10m}$

$\rightarrowtail \bold{Effort\;=\;100kgf}$

$\large\text{To\;find:}$

$\rightarrowtail \bold{Efficiency\;of\;the\;pulley\;system.}$

$\rightarrowtail \bold{Work\;done\;by\;the\;effort.}$

$\large\text{Solution:}$

• Finding the mechanical advantage using the formula:

$\Rrightarrow \bold{Mechanical\;advantage=\dfrac{Load}{Effort} }$

$\hookrightarrow \bold{M.A=\dfrac{300kgf}{100kgf} }$

∴ $\bold{Mechanical\;advantage=3}$

• We already have the velocity ratio, finding the efficiency using the formula:

$\Rrightarrow \bold{Efficiency=\dfrac{M.A}{V.R}\times100\% }$

$\hookrightarrow \bold{Efficiency=\dfrac{3}{4}\times1 }$

∴ $\bold{Efficiency=0.75}$

• First finding the displacement of effort using the formula:

$\Rrightarrow\bold{Velocity\;ratio=\dfrac{Displacement\;of\;effort}{Displacement\;of\;load} }$

$\hookrightarrow \bold{4=\dfrac{Displacement\;of\;effort}{10} }$

∴ $\bold{Displacement\;of\;effort=40m}$

• Now finding the work done by the effort using the formula:

$\Rrightarrow\bold{Work\;done\;by\;the\;effort=Force\;of\;effort \times\; displacement\;of\;effort}$

$\hookrightarrow \bold{Work\;done\;by\;the\;effort=100\;\times40}$

∴ $\bold{Work\;done\;by\;the\;effort=4000J}$

$\large\text{Answers:}$

$\Rightarrow \bold{Efficiency=0.75}$

$\Rightarrow \bold{Work\;done\;by\;the\;effort=4000J}$

$\large\text{Learn\;more:}$

• Mechanical advantage: While using a machine to overcome a certain load, if the effort needed is less than the load, the machine has mechanical advantage greater than 1. While if its needs an effort greater than the load, its has mechanical advantage less than 1. A machine has mechanical advantage equal to 1, if the effort needed is equal to the load. A machines having M.A greater than 1, acts as a force multiplier, while a machine having M.A less than 1, acts as a speed multiplier. A machine with M.A equal to 1, is generally used to change the direction of effort as there is no gain is force or speed.
• Velocity ratio: A machine in which the displacement of load is more than the displacement of effort, will have velocity ratio less than 1 and such a machines gives a gain in speed, and a machine with velocity ratio more than 1 , acts as a force multiplier. If the velocity ratio is equal to 1, then the displacement of load is equal to the displacement of effort.
• Work input: The work done on the machine by the effort.
• Work output: The work done on the machine on the load.
• Efficiency: Efficiency of a machine is the ratio of the work done on the load by the machine to the work done on the machine by the effort. It's formula is Work output/Work input × 100%.

Answer 2

Answer:

Efficiency of the pulley = 0.75

Work done by the Effort.=4000j