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Title: Simple Wheel and Axle Experiment
Aim:
1. To determine the velocity ratio of the machine.
2. To obtain an equation for the relation between load and effort, and hence obtain a value for the limiting efficiency of machine.
Apparatus: Please See your laboratory Manual
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THEORY:
A. Simple Wheel and Axle
In the figure above is shown a Simple wheel & axle, in which the wheel A & axle B are keyed to the same shaft. The shaft is mounted on ball bearings, in order to reduce the frictional resistance to minimum. A string is wound round the axle B, which carries the load to be lifted. A second string is wound round the wheel A in the opposite direction to that of string on B.
Let, W = Load lifted
P = Effort applied to lift the load
D = Diameter of effort wheel, andd
d = Diameter of the load drum
One end of the string is fixed to the wheel, while the other is free and the effort is applied to this end. Since the two strings are wound in the opposite directions, so the downward motion of the effort (P) will raise the load (W). Since the wheel A and axle B are keyed to the same shaft, so when the wheel rotates through one revolution, axle will also rotate through one revolution.
We know that the distance moved by the effort in one revolution the effort wheel = πD & distance moved by the load in one revolution = πd
V.R. = Distance moved by effort / Distance moved by load = πD/ πd = D/ d
Now , M.A. = Load lifted / Effort applied = W/P
and Efficiency η = M.A. / V.R.
B. Differential Wheel and Axle
It is an improved form of Simple wheel & axle, in which the Velocity Ratio is intensified with the help of a load axle. In figure just above is shown a Differential wheel & axle. In this case, load axle BC is made up of two parts of different diameters. Like Simple wheel & axle, the wheel A, & axle B and C are keyed to the same shaft, which is mounted on ball bearings, in order to reduce the frictional resistance to minimum.
The effort string is wound round the wheel A. Another string is wound round the axle B, which after passing round the pulley (to which the weight W is attached) is wound round the axle C in the opposite directions to that of the axle B; care being taken to wind the string on the wheel A & axle C in the same direction. As a result of this, when the string unwinds from the wheel A, the other string also unwinds from the axle C. But it winds on the axle B in the figure above.
Let D = diameter of effort wheel A,
d1 = diameter of the axle B
d2 = diameter of the axle C
W = Weight lifted by the machine, &
P = Effort applied to lift the weight
We know distance moved by the effort in one revolution of the effort wheel A= πD
Therefore, Length of string, which will wound on the axle B in one revolution = πd1
& Length of string, which will unwound from the axle C in one revolution = πd2
Therefore, Length of string, which will wound in one revolution = πd1 - πd2 = π(d1 - d2)
& distance moved by the weight = 1/2× π (d1 - d2) = π/2(d1 - d2)
therefore, V.R. = Distance moved by effort P/ Distance moved by load = πD/ π/2(d1 - d2) = 2D/(d1 - d2)
and, M.A.= W/ P
and, Efficiency, η = M.A./ V.R.
For Procedures, See your Mechanical Laboratory Manual.
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Observations :-
1.
Applications:-
PRECAUTIONS:
For Precautions, See General Laboratory Precautions
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