Machine

Machine is the device that makes our work easier, changes the direction of the force and does the work efficiently.

M.A =  $\frac{{{\rm{\: \: load\: }}}}{{{\rm{effort\: }}}}$

It has no unit.

Velocity ratio

The ratio of the distance moved by the effort to the distance moved by the load is called velocity ratio.

Velocity ratio   =  $\frac{{{\rm{\: distance\: moved\: by\: effort\: }}}}{{{\rm{distance\: moved\: by\: the\: load}}}}$

Efficiency of the machine

It is defined as the ratio of work done by the machine to the work done in the machine.

Efficiency = ${\rm{\: \: }}\frac{{{\rm{\: work\: done\: by\: the\: machine\: \: }}}}{{{\rm{work\: done\: on\: the\: machine\: }}}}$

In other way, it can be defined as the ratio of output work to the input work. It is expressed in terms of percentage.

Efficiency = ${\rm{\: \: }}\frac{{{\rm{\: output\: work\: \: \: }}}}{{\begin{array}{*{20}{c}}{input\: \: work}\\\:\end{array}}}$*100%

An ideal or perfect machine has output work equal to the input work and its efficiency is 100%.But in practice, no such machine exists, so, the efficiency of machine is always less than 100%

Relation between M.A, V.R, and Efficiency

We have,

Efficiency = ${\rm{\: \: }}\frac{{{\rm{\: output\: work\: \: \: }}}}{{\begin{array}{*{20}{c}}{input\: \: work}\\\:\end{array}}}$*100%

=$\frac{{{\rm{load*distance\: moved\: by\: the\: load\: }}}}{{\begin{array}{*{20}{c}}{effort*distance\:moved\: by\: the\: effort}\\{}\end{array}}}$*100%

Efficiency  =$\frac{{\: \: \: \: {\bf{M}}.{\bf{A}}}}{{{\bf{V}}.{\bf{A}}}}$  *100%

Pulley

Pulley is a wheel   made of up wood or metal that rotates on its axle. It has groove in its circumference through which a rope can be passed easily.

There are mainly two types:

Single fixed pulley: It is the type of pulley in which the load is raised directly upward. Load is placed at the one end and effort is applied at the other end .Here the effort applied moves   down the distance l and the load moves up the distance l.

In the absence of friction

Input work    = output work

E*l=L*l

L/E=1

M.A =1

Also the V.R = distance moved by the effort /distance moved by the load

= l/l

=1

So .the efficiency =100% for the single fixed pulley.

In this type of pulley load and effort are equal. There is no gain mechanical advantage .

Single movable pulley: In this pulley, there are two wheels, one fixed and other movable. Effort is applied on the free end of rope and the load is total upward force is 2 times the effort

M.A for this pulley is 2

V.R =2

Therefore, Efficiency =100%

But in real practice efficiency is always less than 100%

In general, V.R is equal to number of pulley used.

Inclined plane

It is machine which is used to lift the heavy object to a height.

M.A =  $\frac{{{\rm{the\: \: distance\: moved\: in\: aplane\: surface}}.{\rm{\: }}}}{{{\rm{the\: actual\: height\: \: through\: which\: load\: is\: raised}}}}$

=${\rm{\: \: }}\frac{{\rm{l}}}{{\rm{h}}}$

V.R = $\frac{{{\rm{distance\: moved\: byt\: he\: effort\: in\: an\: inclined\: plane}}}}{{{\rm{distance\: \: moved\: by\: load\: vertically\: upward}}}}\frac{{\rm{l}}}{{\rm{h}}}$

Putting the value,

Efficiency  =$\frac{{{\rm{M}}.{\rm{A}}}}{{{\rm{V}}.{\rm{A}}}}$*100% = 100%

Wheel and axle

Wheel and axle consists of two co axial cylinder .Large one is called wheel and small one is called axle.

M.A = $\frac{{{\rm{radius\: of\: wheel\: }}}}{{{\rm{radius\: of\: axle\: }}}}$

V.R = $\frac{{{\rm{distance\: moved\: by\: effort\: }}}}{{{\rm{distane\: moved\: by\: t\: he\: load}}}}$ = $\frac{{{\rm{radius\: of\: wheel\: }}}}{{{\rm{radius\: of\: axle\: }}}}$

Efficiency  =$\frac{{{\rm{M}}.{\rm{A}}}}{{{\rm{V}}.{\rm{A}}}}$*100%

Moment

Moment of the force may be defined as the product of the force and its perpendicular distance of the line of action from the axis of rotation.

Moment = f*d

Law of moment

It states that “In the balanced condition the sum of the clockwise moment acting on it is equal to the sum of anti clockwise moment on it”.

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