8. WHEEL AND AXLE PDF

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EIGHTH PRACTICAL WHEEL AND AXLE...

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8. WHEEL AND DIFFERENTIAL AXLE

AIM: To determine velocity ratio, mechanical advantage and efficiency of wheel and differential axle.

APPARATUS: Wheel and differential axle, hooks, strings, weights, scale etc.

THEORY: This system consists of a differential axle of diameter d 1 and d2 (d2 greater than d1) and a wheel of diameter D, fixed uniaxially as shown in the figure. One end of the rope is tied to the pin provided on the axle portion having diameter d 1 and a part of the rope is wound around it. The other end of the rope is wound around axle on the portion having diameter d 2 in the opposite direction. This pattern of winding forms a loop and a simple pulley is installed in this loop as shown in the Fig. The load is attached to this pulley. The second rope is wound to the wheel in such a direction that if it is unwound, the rope around the bigger diameter axle gets wound up and rope around smaller diameter axle gets unwound. One end of this second rope provides means for application of the effort. Suppose the whole system makes one complete revolution due to the applied effort, then Total distance moved by the effort at the differential axle =  D Length of winding of the rope =  d2 Length of unwinding of rope =  d1 ∴ Net wound length =  d2 -  d1 =  (d2-d1) But, the rope is continuous and the load is to be lifted by the pulley block in the loop. Total height over which pulley is lifted =  (d2-d1) / 2 Therefor the distance moved by the load =  (d2-d1) / 2  VR =  D / (  (d2-d1) / 2)

= 2D / (d2-d1) Hence, velocity ratio in wheel and differential axle is given by: VR = 2D / (d2-d1)

PROCEDURE: •

For the first part of the experiment, we have to calculate velocity ratio. The VR can be had by taking any load and enough effort just to bring the system in equilibrium.

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Take two different situations, in one case load is to be kept below the effort and in other situation effort is to be brought below the load.

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In both the situations measure the heights of load and effort from the respective ground level or datum.

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The difference of initial and final heights of load and effort gives us Y and X respectively.

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Calculate Y/X and this is the actual value of VR. Then calculate theoretical value of VR.

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In the second part of the experiment, calculate mechanical advantage.

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For MA calculate actual effort required to lift the given load.

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Note the value of effort against the load.

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Do the necessary calculations and find out MA.

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Tabulate the results obtained.

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Plot the graph of effort vs load & find out slope of it.

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Same way plot the graph of efficiency vs load & find out max efficiency.

OBSERVATIONS: 1) Diameter of wheel (D) = 2) Diameter differential axle (d1) = (d2) =...