Simple Machines
$\displaystyle \small \bullet$ A machine is a mechanical device by means of which a force applied at one point is transmitted to another point in order to move a load.
$\displaystyle \small \bullet$ Ex: jack lifting an automobile van, press operated by hand
Effort
$\displaystyle \small \bullet$ Effort is the force applied to the machine in order to perform work.
$\displaystyle \small \bullet$ It is denoted by 'P'.
Load
$\displaystyle \small \bullet$ The amount of weight lifted or controlled by a machine is called load.
$\displaystyle \small \bullet$ It is denoted by 'W'.
Mechanical Advantage
$\displaystyle \small \bullet$ The ratio of load lifted to effort applied is known as mechanical advantage.
$\displaystyle \small \bullet$ Its value should be more than 1.
$\displaystyle \small Mechanical\; Advantage=\frac{Load}{Effort}$
$\displaystyle \small M.A.=\frac{W}{P}$
Velocity Ratio
$\displaystyle \small \bullet$ Velocity ratio of a machine is defined as the ratio of the distance moved by object due to effort to the distance moved by the load.
$\displaystyle \small V.R.=\frac{d_{P}}{d_{W}}$
Output and Input
$\displaystyle \small \bullet$ The product of load and distance moved by load is known as output.
Output = Load✕Distance moved by the load
$\displaystyle \small \bullet$ The product of effort and distance moved by effort is known as input.
Input = Effort✕Distance moved by object due to effort
Efficiency of Machine
$\displaystyle \small \bullet$ The ratio of output to the input of machine is known as efficiency.
$\displaystyle \small \bullet$ In simple machines, the ratio of mechanical advantage to the velocity ratio is known as efficiency of machine.
$\displaystyle \small \bullet$ It is generally expressed in percentage.
$\displaystyle \small Efficiency(\eta )=\frac{Output}{Input}$
$\displaystyle \small \eta=\frac{Wd_{W}}{Pd_{P}}$
%$\displaystyle \small \eta =\frac{M.A.}{V.R.}\times 100$
$\displaystyle \small \bullet$ Efficiency of an ideal machine is 100% or $\displaystyle \small \eta=1$
⇒ M.A=VR
⇒ Wd=PD
Types of Simple Machines
1. Pulley
2. Inclined plane
3. Wheel and axle
4. Differential wheel and axle
5. Screw jack
Lever
$\displaystyle \small \bullet$ The lever consists of a rigid rod, which can turn freely about a fixed point, known as fulcrum.
$\displaystyle \small \bullet$ Effort arm: perpendicular distance from fulcrum to the lines of action of effort.
$\displaystyle \small \bullet$ Load arm: perpendicular distance from fulcrum to the lines of action of load.
$\displaystyle \small \bullet$ Principle of levers
Load✕Load arm = Effort✕Effort arm
$\displaystyle \small \bullet$ Classification:
$\displaystyle \small \circ$ Straight levers
$\displaystyle \small \circ$ Curved levers
Straight Levers
$\displaystyle \small \bullet$ Classification
$\displaystyle \small \circ$ First order lever
$\displaystyle \small \blacktriangle$ The fulcrum is between the effort and the load.
$\displaystyle \small \blacktriangle$ Ex: Scissors, beams of a common balance, claw hammer, handle of a tubewell pump, plier and cycle brake.
$\displaystyle \small \circ$ Second order lever
$\displaystyle \small \blacktriangle$ Load is placed between the effort and the fulcrum.
$\displaystyle \small \blacktriangle$ Ex: Nut cracker, wheel barrow, crowbar when rowing, pinch bar used to turn a load and oar of a boat.
$\displaystyle \small \circ$ Third order lever
$\displaystyle \small \blacktriangle$ Effort is between the load and the fulcrum.
$\displaystyle \small \blacktriangle$ Ex: Coal tongs, Human forearm, a safety valve lever and a fishing rod.
Curved Levers
$\displaystyle \small \bullet$ In this type of levers, both arms are bent $\displaystyle \small 0^{0}$ to $\displaystyle \small 180^{0}$.
$\displaystyle \small \bullet$ Ex: Bell cranked lever, in which arms are usually bent at $\displaystyle \small 90^{0}$.
Application of Levers
$\displaystyle \small \bullet$ Levers of different order are combined together in machines.
$\displaystyle \small \bullet$ Combination of first and second order is used in typewriter.
$\displaystyle \small \bullet$ Combination of different order of levers found in applying brakes to motor bike, cycle and instruments like aneroid barometer etc.
$\displaystyle \small \bullet$ A machine is a mechanical device by means of which a force applied at one point is transmitted to another point in order to move a load.
$\displaystyle \small \bullet$ Ex: jack lifting an automobile van, press operated by hand
Effort
$\displaystyle \small \bullet$ Effort is the force applied to the machine in order to perform work.
$\displaystyle \small \bullet$ It is denoted by 'P'.
Load
$\displaystyle \small \bullet$ The amount of weight lifted or controlled by a machine is called load.
$\displaystyle \small \bullet$ It is denoted by 'W'.
Mechanical Advantage$\displaystyle \small \bullet$ The ratio of load lifted to effort applied is known as mechanical advantage.
$\displaystyle \small \bullet$ Its value should be more than 1.
$\displaystyle \small Mechanical\; Advantage=\frac{Load}{Effort}$
$\displaystyle \small M.A.=\frac{W}{P}$
Velocity Ratio
$\displaystyle \small \bullet$ Velocity ratio of a machine is defined as the ratio of the distance moved by object due to effort to the distance moved by the load.
$\displaystyle \small V.R.=\frac{d_{P}}{d_{W}}$ Output and Input
$\displaystyle \small \bullet$ The product of load and distance moved by load is known as output.
Output = Load✕Distance moved by the load
$\displaystyle \small \bullet$ The product of effort and distance moved by effort is known as input.
Input = Effort✕Distance moved by object due to effort
Efficiency of Machine
$\displaystyle \small \bullet$ The ratio of output to the input of machine is known as efficiency.
$\displaystyle \small \bullet$ In simple machines, the ratio of mechanical advantage to the velocity ratio is known as efficiency of machine.
$\displaystyle \small \bullet$ It is generally expressed in percentage.
$\displaystyle \small Efficiency(\eta )=\frac{Output}{Input}$
$\displaystyle \small \eta=\frac{Wd_{W}}{Pd_{P}}$
%$\displaystyle \small \eta =\frac{M.A.}{V.R.}\times 100$
$\displaystyle \small \bullet$ Efficiency of an ideal machine is 100% or $\displaystyle \small \eta=1$
⇒ M.A=VR
⇒ Wd=PD
Types of Simple Machines
1. Pulley
2. Inclined plane
3. Wheel and axle
4. Differential wheel and axle
5. Screw jack
Lever
$\displaystyle \small \bullet$ The lever consists of a rigid rod, which can turn freely about a fixed point, known as fulcrum.
$\displaystyle \small \bullet$ Effort arm: perpendicular distance from fulcrum to the lines of action of effort.
$\displaystyle \small \bullet$ Load arm: perpendicular distance from fulcrum to the lines of action of load.
$\displaystyle \small \bullet$ Principle of levers
Load✕Load arm = Effort✕Effort arm
$\displaystyle \small \bullet$ Classification:
$\displaystyle \small \circ$ Straight levers
$\displaystyle \small \circ$ Curved levers
Straight Levers
$\displaystyle \small \bullet$ Classification
$\displaystyle \small \circ$ First order lever
$\displaystyle \small \blacktriangle$ Ex: Scissors, beams of a common balance, claw hammer, handle of a tubewell pump, plier and cycle brake.
$\displaystyle \small \circ$ Second order lever
$\displaystyle \small \blacktriangle$ Load is placed between the effort and the fulcrum.$\displaystyle \small \blacktriangle$ Ex: Nut cracker, wheel barrow, crowbar when rowing, pinch bar used to turn a load and oar of a boat.
$\displaystyle \small \circ$ Third order lever
$\displaystyle \small \blacktriangle$ Effort is between the load and the fulcrum.$\displaystyle \small \blacktriangle$ Ex: Coal tongs, Human forearm, a safety valve lever and a fishing rod.
Curved Levers
$\displaystyle \small \bullet$ In this type of levers, both arms are bent $\displaystyle \small 0^{0}$ to $\displaystyle \small 180^{0}$.
$\displaystyle \small \bullet$ Ex: Bell cranked lever, in which arms are usually bent at $\displaystyle \small 90^{0}$.
Application of Levers$\displaystyle \small \bullet$ Levers of different order are combined together in machines.
$\displaystyle \small \bullet$ Combination of first and second order is used in typewriter.
$\displaystyle \small \bullet$ Combination of different order of levers found in applying brakes to motor bike, cycle and instruments like aneroid barometer etc.
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