Revision: Force, Work, Power and Energy >> Machines Physics (English Medium) ICSE Class 10 CISCE

The work done by the machine on the load is called work output (W_output).

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.

or

Efficiency is the ratio of work output to work input. It is denoted by the symbol (η).

It is the proportion of the machine's useful work to the effort's input into the machine.

Efficiency η = `"Work output"/"Work input" xx 100%`

The ratio of the velocity of effort to the velocity of the load is called the velocity ratio of the machine.

Velocity ratio (V.R.) = `("Velocity of effort"  ("V"_"E"))/("Velocity of load"  ("V"_"L"))` 

The ratio of the velocity of effort to the velocity of load is called the velocity ratio of the machine.

The work done on the machine by the effort is called work input (W_input).

The resistive or opposing force to be overcome by a machine is called load (L). 

The force applied on the machine to overcome the load is called effort (E).

The ratio of load to effort is called the mechanical advantage of the machine

The point at which energy is supplied to a machine by applying effort is called the effort point.

The point where energy is obtained by overcoming the load is called the load point.

 Lever: A lever is a rigid, straight or bent bar which is capable of turning about a fixed axis.

A lever is a rigid, straight (or bent) bar which is capable of turning about a fixed axis.

A pulley which has its axis of rotation stationary in position, is called a fixed pulley.

A Pulley whose axis of rotation is movable (i.e., not fixed in position) is called a movable pulley.

Mechanical advantage (M.A.) = \[\frac{Load\left(L\right)}{Effort\left(E\right)}\]

\[\text{Velocity Ratio (V.R.)}=\frac{\text{Velocity of Effort }(V_E)}{\text{Velocity of Load }(V_L)}\]

or

\[\mathrm{V.R.}=\frac{d_{E}}{d_{L}}\]

\[\text{Efficiency n}=\frac{\text{Work output}(\mathrm{W}_{output})}{\mathrm{Work~input}(\mathrm{W}_{input})}\]

or

\[{\text{Efficiency }\eta=\frac{\text{Work output}(\mathrm{W}_{output})}{\mathrm{Work~input}(\mathrm{W}_{input})}\times100\%}\]

Input Energy = Effort × Displacement of Effort

Output Energy = Load × Displacement of Load

Functions and Uses of Simple Machines:

• In lifting a heavy load by applying less effort, i.e., as a force multiplier.
• In changing the point of application of effort to a convenient point.
• In changing the direction of effort to a convenient direction. 
• For obtaining a gain in speed (i.e., a greater movement of load by a smaller movement of effort).

• Output Energy = Input Energy

• Ideal Machine:
  An ideal machine is one in which no energy is lost in any manner. Here, the work output equals the work input, i.e., the efficiency of an ideal machine is 100%.

• Actual Machine:
  In an actual machine, the output energy is always less than the input energy, i.e., there is always some loss of energy during its operation.

• Reasons for Energy Loss in an Actual Machine:
  The loss of energy in a machine is due to the following three reasons:
  (1) the moving parts in it are neither weightless nor smooth (or frictionless),
  (2) the string in it (if any) is not perfectly elastic, and
  (3) Its different parts are not perfectly rigid.

• The mechanical advantage of a lever is equal to the ratio of the length of its effort arm to the length of its load arm.
  or
  \[{\mathrm{M.A.}=\frac{\text{Effort arm FA}}{\text{Load arm FB}}}\]
• The mechanical advantage of a lever can be increased either by increasing its effort arm or by decreasing its load arm.

• For class I levers, the mechanical advantage and velocity ratio can have any value, either greater than 1, equal to 1, or less than 1.
• The mechanical advantage and velocity ratio of class II levers are always more than 1.
• The mechanical advantage and velocity ratio of class III levers are always less than 1.

• It is a metallic (or wooden) disc with a grooved rim.
• A string or rope is passed around the groove at the rim. The disc rotates about an axle passing through its centre. The axle is fixed rigidly to a frame by means of nails.
• A single pulley can be used in two ways:
  (1) a fixed pulley
  (2) a movable pulley

• Mechanical Advantage = \[\frac {\text{load L}}{\text{effort E}}\] = \[\frac {T}{T}\] = 1
  Thus, in this arrangement, there is no gain in mechanical advantage.
• \[{\therefore\text{ Velocity ratio}=\frac{d_E}{d_L}=\frac{d}{d}=1}\]
• Efficiency η = \[\frac {M.A.}{V.R.}\] = 1 or 100%
• A fixed pulley is used only to change the direction of effort to be applied, i.e., with its use, the effort can be applied in a more convenient direction.

• M.A. = \[\frac {2T}{T}\] = 2
• V.R. = \[\frac {d}{d/2}\] = 2
• Efficiency η = \[\frac {M.A.}{V.R.}\] = \[\frac {2}{2}\] = 1 or 100%
• A movable pulley is used as a force multiplier.

• In a fixed pulley, the axis remains stationary, and the load moves opposite to the effort.
• In a movable pulley, the axis moves, and the load moves in the same direction as the effort.

• A combination of pulleys is used to lift heavy loads when the required mechanical advantage (M.A.) exceeds 2.
• Two types: (1) One fixed pulley with several movable pulleys, (2) Block and tackle system with pulleys in two blocks.

• For n movable pulleys with one fixed pulley, M.A. = 2ⁿ and V.R. = 2ⁿ (ideal case).
• In equilibrium, Effort E = T₃ and Load L = 2³ × T₃, so M.A. = 2³ for 3 movable pulleys.
• Efficiency = M.A. / V.R. = 2ⁿ / 2ⁿ = 1 or 100% (ideal), but reduced due to pulley weight and friction.

• In a block and tackle system, if total pulleys = n, then M.A. = n and V.R. = n (ideal case).
• Efficiency η = M.A. / V.R. = n / n = 1 or 100%, but it decreases due to the weight of the lower block and friction.
• For greater efficiency, pulleys in the lower block should be light, and bearings should be lubricated.