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AIM: To study the performance of differential axle & wheel and find its velocity ratio, efficiency and law of machine etc.
EQUIPMENTS REQUIRED:
Differential axle and wheel consisting of effort wheel,
Threads,
Pan,
Weights.
THEORY:
The simplest machine which is in use, since ages is the simple wheel and axle used for drawing up water from well. It is used on the village wells even till date. Simple wheel and axle are used to lift loads. Simple wheel and axle consist of an effort wheel and an axle of different diameters which are keyed to same spindle. The diameter of the wheel is greater than the diameter of the axle to reduce the frictional resistance.
Since the two strings are wound in opposite directions, therefore, a downward motion of P will lift the load W.
Let D = Diameter of the effort wheel,
d1 & d2 = Diameter of axle,
W = Load lifted and
P = Effort applied to lift the weight
Since the wheel and axle are mounted on the same spindle. In one revolution of the wheel, the axle will also make one revolution.
Distance moved by load in one revolution = π d
Distance moved by effort in one revolution = π D
V.R = Distance moved by Effort
Distance moved by Load
2 D
V.R = (d1- d2)
Now Mechanical Advantage (M.A.) = W/P
Efficiency( ᶯ) = M.A / V.R
PROCEDURE:
1. Measure the diameter of the wheel as D with the help of vernier calliper.
2. Measure the diameter of the axle as d1 and d2 of axel with the help of vernier calliper.
3. Wind one string on the effort wheel and attach to pan to carry effort load P.
4. Wind other string on the axle of different diameter to hang load.
5. Now place the weight slowly in the effort pan unless and until the load just starts to lift up
7. Note the weight placed in the effort Pan.
8. Calculate M.A. V.R. and efficiency.
9. Repeat the above procedure by increasing the load in the load pan and note down the corresponding effort.
CONCLUSION: i. As the efficiency is greater than 50%, machine is reversible. ii. Velocity ratio remains constant. iii. Effort of machine increases with load. iv. Graph of effort against load is a straight line represents linear motion. THEORY: Moment of Inertia is the property of the body by virtue of which it resists the change in the state of its angular motion about any axis. It depends upon the mass of the body and the distance with respect to axis of rotation. The flywheel consists of a heavy circular disc/massive wheel fitted with a strong axle projecting on either side. The axle is mounted on ball bearings on two fixed supports. There is a small peg on the axle. One end of a cord is loosely looped around the peg and its other end carries the weight-hanger.
PROCEDURE: 1. Attach a long thread about 1.8 m length to the axle of flywheel and end of thread is attached to the axle while the pan is attached to the outer end of the thread. 2. Weight should be added so that pan must be in suitable line on the wheel by which we can calculate number of revolutions of the wheel. 3. Wrap the thread on the axle and measure the height of the pan from the ground level, and then add the weights in the pan and take readings of time required for pan to touch the ground. 4. This time is calculated by using the stop watch as soon as weight starts moving down. 5. The length of the cord is carefully adjusted, so that when the weight-hanger just touches the ground, the loop slips off the peg. A suitable weight is placed in the weight hanger. A chalk mark is made on the rim so that it is against the pointer when the weight hanger just touches the ground. 7. The other end of the cord is loosely looped around the peg keeping the weight hanger just touching the ground. The flywheel is given a suitable number (n) of rotation so that the cord is wound round the axle without overlapping.