Question

The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Kinetic energy of the flywheel after 10 seconds from the start.

(a) 50 kJ

(b) 60 kJ

(c) 45 kJ

(d) none of the mentioned

I got this question during an online interview.

This intriguing question comes from Numericals On Kinetics Of Motion and Loss of Kinetic Energy in portion Kinematics & Kinetics of Motion of Machine Kinematics

Answer 1

The correct answer is (c) 45 kJ

The explanation: Given : k = 1 m ; m = 2500 kg ; T = 1500 N-m

 Angular acceleration of the flywheel

Let α = Angular acceleration of the flywheel.

We know that mass moment of inertia of the flywheel,

I=m.k^2 = 2500×12 = 2500 kg-m^2

We also know that torque ( T ),

1500 = I .α = 2500 × α

or α = 1500 / 2500 = 0.6 rad/s^2

Kinetic energy of the flywheel after 10 seconds from start

First of all, let us find the angular speed of the flywheel (ω^2) after t = 10 seconds from the start (i.e. ω^1 = 0 ).

We know that ω^2 = ω^1 + α.t = 0 + 0.6 × 10 = 6 rad/s

∴ Kinetic energy of the flywheel,

E = 1/2 I(ω^2)^2

  = 1/2 x 2500 x 6^2

  = 45 000J

  = 45 kJ