Question

The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the acceleration of the piston, when it is at a distance of 0.75 metre from the centre.

(a) 118.46 m/s^2

(b) 90 m/s^2

(c) 100 m/s^2

(d) none of the mentioned

The question was posed to me in a national level competition.

This intriguing question originated from Centre of Percussion in chapter Simple Harmonic Motion of Machine Kinematics

Answer 1

Correct answer is (a) 118.46 m/s^2

The explanation: Given : N = 120 r.p.m. or ω = 2π × 120/60 = 4π rad/s ; 2r = 2 m or r = 1 m;

x = 0.75 m

Velocity of the piston

We know that velocity of the piston,

v = ω√r^2 – x^2 = 4π√1 – (0.75)^2 = 8.31 m/s

We also know that acceleration of the piston,

a = ω^2.x = (4π)^2 0.75 = 118.46 m/s^2.