# With the help of a belt an engine running at 200 rpm drives a line shaft. The Diameter of the pulley on the engine is 80 cm

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With the help of a belt an engine running at 200 rpm drives a line shaft. The Diameter of the pulley on the engine is 80 cm and the diameter of the pulley on the line shaft is 40 cm. A 100cm diameter pulley on the line shaft drives a 20 cm diameter pulley keyed to a dynamo shaft. Find the speed of the dynamo shaft when: (1) There is no slip (2) There is a slip of 2.5% at each drive.

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Dia. of driver pulley (D1) = 80cm

Dia. of follower pulley (D2) = 40cm

Dia. of driver pulley (D3) = 100cm

Dia. of follower pulley (D4) = 20cm

Slip on each drive, s1 = s2 = 2.5

Let N4 = Speed of the dynamo shaft

(i) When there is no slip

Using equation

N4/N1 = (D1.D3)/(D2.D4)

N4 = N1 X (D1.D3)/(D2.D4)

= [(80 X 100) X 200]/(40 X 20)

N4 = 2000RPM

(ii) When there is a slip of 2.5% at each drive In this case we will have the equation of:

N4/N1 = [(D1.D3)/(D2.D4)][1–s1/100][1–s2/100] Putting all the values, we get

N4 = N1 X [(D1.D3)/(D2.D4)][1– s1/100][1– s2/100]

N4 = 200 X [(80 X 100)/(40 X 20)][1 – 2.5/100][1– 2.5/100]

N4 = 1901.25R.P.M