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Simple Lifting machine, A Simple lifting machine can be defied as a device which is used to lift heavy loads by applying a, small effort in a convenient direction., Example: pulley used to lift water form well, screw jack used to lift motor car etc., , Simple Machine: it is defined as a device that receives some energy and uses it for doing a, particular useful work., Example: IC Engine converts the energy provided by gasoline into motion., , Compound Machine: it is the combination of more than one simple machine which enables us to do, some useful work at a faster speed or with a much less effort as compared to a simple machine., , Basic Definitions:, Load(W): Any weight which is lifted by machine., Effort(P): A force required to lift a load., Mechanical Advantages (M.A): It is the ratio of weight lifted (W) to the effort applied (P)., M.A=, , 𝑙𝑜𝑎𝑑 𝑙𝑖𝑓𝑡𝑒𝑑, 𝑒𝑓𝑓𝑜𝑟𝑡 𝑎𝑝𝑝𝑙𝑖𝑒𝑑, , =, , 𝑊, 𝑃, , Velocity ratio (V.R): The ratio of distance moved by effort(y) to the distance moved by load(x)., , 𝑦, V.R=, , 𝑥, , INPUT OF A MACHINE: The input of a machine is the work done on the machine. In a lifting machine, it, is measured by the product of effort and the distance through which it has moved., INPUT= effort*distance moved by effort = P*y, , OUTPUT OF A MACHINE: The output of a machine is the actual work done by the machine. In a lifting, machine, it is measured by the product of the weight lifted and the distance through which it has been, lifted., OUTPUT= load lifted* distance moved by load= W*x, , EFFICIENCY OF A MACHINE It is the ratio of output to the input of a machine and is generally expressed, as a percentage., Mathematically, efficiency, η(Eta)=, , 𝑂𝑈𝑇𝑃𝑈𝑇, 𝐼𝑁𝑃𝑈𝑇, , ∗ 100

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RELATION BETWEEN EFFICIENCY, MECHANICAL ADVANTAGE AND VELOCITY RATIO OF A LIFTING, MACHINE:, Let,, W = Load lifted by the machine,, P = Effort required to lift the load,, Y = Distance moved by the effort in lifting the load, x = Distance moved by the load, , M.A=, , We know,, , 𝑙𝑜𝑎𝑑 𝑙𝑖𝑓𝑡𝑒𝑑, 𝑒𝑓𝑓𝑜𝑟𝑡 𝑎𝑝𝑝𝑙𝑖𝑒𝑑, V.R=, , η(Eta)=, , 𝑂𝑈𝑇𝑃𝑈𝑇, 𝐼𝑁𝑃𝑈𝑇, , =, , =, , 𝑊, 𝑃, , 𝑦, 𝑥, , = load lifted∗ distance moved by load, effort∗distance moved by effort, , =, , =, , W∗x, P∗y, , 𝑊 1, 𝑀. 𝐴, ∗𝑦 =, 𝑃, ൗ𝑥 𝑉. 𝑅, 𝑀.𝐴, , η= 𝑉.𝑅, Ideal Machine:, , A machine whose efficiency is 1 (i.e., 100%) is called an ideal machine. In other words, in an ideal machine,, the output is equal to the input., in an ideal machine, Velocity Ratio = Mechanical Advantage, , Ideal Effort:, Ideal effort is the effort required to lift the given load by the machine assuming the machine to be ideal., For ideal machine, VR = MA, If Pi is the ideal effort,, , then VR =, , Hence, 𝑃𝑖, , =, , 𝑊, 𝑃𝑖, 𝑊, 𝑉.𝑅

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Ideal Load:, Ideal load is the load that can be lifted using the given effort by the machine, assuming it to be ideal., For the ideal machine, VR = MA, If Wi is the ideal load, then, , 𝑊𝑖 = 𝑃 ∗ 𝑉. 𝑅, , REVERSIBILE AND IRREVERSIBLE MACHINE:, If the removal of effort while lifting results in lowering of the load, the machine is said to be reversible., Example: While lifting water from the well, the pot falls back if the effort to pull it up is removed, The machine is said to be self-locking or irreversible if the load is not lowered on removal of the effort., Example: The screw jack used to lift the motor car will hold the car at the same position even if the, application of the effort is stopped., A simple lifting machine will be reversible or self-locking solely based on its efficiency. It can be shown, that a lifting machine is reversible if its efficiency is greater than 50 per cent and self-locking if its efficiency, is less than 50 per cent., , Condition for reversible machine:, Let,, W – load being lifted, P – effort required, VR – Velocity ratio, y – distance moved by the effort., x – distance moved by the load, Work lost in friction =Input -Output= (P × y) – (W × x), When effort is removed, the load can start moving down if it can overcome the, frictional resistance= (P × y) – (W × x), Hence the condition for the reversibility is: (W × x)> (P × y) – (W × x),  2W×x>P×y,  (W/P) (x/y)>1/2,  M.A× (1/V. R) >1/2, ,  η > 1/2 or 50%, Hence, a machine is reversible if its efficiency is greater than 50%., Note: condition for a machine to be non-reversible or self-locking is that its efficiency should not, be more than 50%.

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LAW OF MACHINE:, The relationship between the load lifted and the effort required in a machine is called the law of machine., This is found by conducting experiments in which efforts required for lifting different loads are determined, and then load versus effort graph as shown in Fig., , The law of a lifting machine is given by the relation : P = mW + C, where P = Effort applied to lift the load,, m = A constant (called coefficient of friction) which is equal to the slope of the line AB,, W= Load lifted, C = Another constant, which represents the machine friction, (i.e. OA)., , FRICTION IN MACHINE:, Friction exists between all surfaces of contacts of movable parts. Some of the work done by the, effort is utilised to overcome frictional resistance. Hence, the useful work done in lifting the load, is reduced, resulting in reduction of efficiency., P = actual effort required, Pi = ideal effort required, W = actual load to be lifted, Wi = ideal load to be lifted

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MAXIMUM MECHANICAL ADVANTAGE OF A LIFTING MACHINE:

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MAXIMUM EFFICIENCY OF A LIFTING MACHINE