Question

For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of K.E per cycle is found to be 2 KJ. What is the least possible mass of the flywheel if it diameter is not exceeding 1 m?

1. 40 kg
2. 51 kg
3. 62 kg
4. 73 kg

Answer 1

Correct Answer - Option 2 : 51 kg

Concept:

\(E_f=Iω^2K_S\)

where E_f = Fluctuation of energy, I = Mass moment of inertia, ω = Mean speed of rotation, K_s = Coefficient of fluctuation of speed

Mass moment of inertia for a solid disc;

\(I = \frac{mr^2}{2}\)

where m = mass of the disc, r = radius of the disc

Calculation:

Given:

E_f = 2 kJ = 2000 J, K_s = 2 % = 0.02,

Diamter = 2 × Radius = 1 m

Radius (r) = 0.5 m

Mean speed (N) = 1200 rpm 

\(\omega = \frac{2\pi N}{60} =\frac{2\times \pi \times1200}{60} = 125.66\ rad\)

∴ \(2000=\frac{m\times(0.5)^2\times(125.66)^2\times(0.02)}{2}\)

m = 50.663 kg

Hence the mass of the flywheel should be near 50.66 kg.