Jatinder Singh Solutions for Chapter: Machines, Exercise 1: Expected Questions

The handle of a nut-cracker is $16 \mathrm{cm}$ long and a nut is placed $2 \mathrm{cm}$ from its hinge. If a force of $4 \mathrm{kgf}$ is applied at the end of handle to crack it, what weight, if simply, placed on the nut will crack it ?

Calculate: -
$\left(\mathrm{i}\right)$ velocity ratio,
$\left(\mathrm{ii}\right)$ mechanical advantage,
$\left(\mathrm{iii}\right)$ percentage efficiency of machine which can overcome a resistance of $500 \mathrm{N}$ through a distance of $0.12 \mathrm{m}$, when an effort of $100 \mathrm{N}$ acts through a distance of $0.72 \mathrm{m}$.

An effort of $500 \mathrm{N}$ is applied through a distance of $0.50 \mathrm{m}$ on a machine, whose efficiency is $90\%$ such that resistance is overcome through a distance of $0.04 \mathrm{m}$. Calculate: -
 $\left(\mathrm{i}\right)$ velocity ratio,
 $\left(\mathrm{ii}\right)$ mechanical advantage,
 $\left(\mathrm{iii}\right)$ resistance overcome by the machine.

A pulley system has $5$ pulleys in all and is $90\%$ efficient.Calculate: -
$\left(\mathrm{i}\right)$ The mechanical advantage,
$\left(\mathrm{ii}\right)$ The effort to lift a body of $1000 \mathrm{N}$,
$\left(iii\right)$ The resistance due to the movable parts of the machine and friction.

A car develops a force of $500 \mathrm{N}$ and climbs up a vertical distance $200 \mathrm{m}$. If the load due to the car is $12500 \mathrm{N}$, calculate the length of the road covered by the car.

A fire tong has its arms $20 \mathrm{cm}$ long. It is used to lift a coal of weight $1.5 \mathrm{kgf}$by applying an effort at distance $15 \mathrm{cm}$ from fulcrum.
Find: Mechanical advantage.

A fire tong has its arms $20 \mathrm{cm}$ long. It is used to lift a coal of weight $1.5 \mathrm{kgf}$ by applying an effort at a distance $15 \mathrm{cm}$ from fulcrum.
Find: Effort needed.

Draw a labelled diagram of a block and tackle pulley having a $\mathrm{V}.\mathrm{R}. 5$. If load of $500 \mathrm{N}$ is raised through a distance of $2 \mathrm{m}$ by an effort of $160 \mathrm{N}$, Find:
(a) Efficiency,
(b) Resistance wasted in the machine.