# Numerical - Power transmitted in brake, given drum diameter - Theory of Machines - 1

Q.  Determine the power transmitted if dead weight on brake is 70 kg and engine has a speed of 300 rpm. One end of the rope has a diameter of 0.05 m is attached to a spring balance which has reading of 150 N, diameter of drum is 1 m.
- Published on 06 Aug 15

a. 8.851 kW
b. 8.851 W
c. 1319.46 W
d. none of the above

#### Discussion

• Sravanthi   -Posted on 19 Oct 15
Rope brake dynamometer is an absorption dynamometer. Number of ropes are wrapped over the pulley rim and keyed to the shaft of the engine. One end of rope is attached to spring balance and and other end to the dead weight.

Given: Dead weight on brake = 70 kg, speed of engine = 300 rpm, rope diameter = 0.05 m, reading on spring balance = 150 N, drum diameter = 1 m

At constant speed torque transmitted by the engine is equal to frictional torque of ropes.

Formula : Brake power = [(W - S) π (D + d) N] / 60 Watt

where,

W = dead weight
S = spring balance reading
N = speed of engine
D = drum diameter
d = rope diameter

Solution:

Weight = 70 x 9.81 = 686.7 N

Substituting the given values we get,

Brake power = [(W -S) π (D+d) N] / 60 Watt
= [ (686.7 – 150) π (1 + 0.05) 300] / 60
= 8851.987 W
= 8.851 kW

The power transmitted is 8.851 kW

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