Find speed of dynamo shaft:

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

Sol:

Diameter of driver pulley (D₁) = 80cm 

Diameter of follower pulley (D₂) = 40cm
Diameter of driver pulley (D₃) = 100cm
Diameter of follower pulley (D₄) = 20cm

Slip on each drive, s₁  = s₂  = 2.5

Let N₄ = Speed of dynamo shaft

(i) When there is no slip

By 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                                                            .......ANS

(ii) When there is slip of 2.5 percent at each drive

In this case we will have equation of:

N₄/N₁  = [(D_1.D₃)/(D₂.D4)][1-s1/100][1-s2/100] By putting the values, we get