Question

The piston of the steam engine moves with SHM, the crank rotates at 120 r.p.m.with a stroke of 2m.Find the velocity and acceleration of the piston when it is at a distance of 0.75 meter from the centre?​

Answer 1

Hello Dear,

◆ Answer -

At x = 0.75 m from the centre,

Velocity = 8.315 m/s

Acceleration = 104.5 m/s

◆ Explaination -

# Given -

Frequency = 120 rpm = 2 Hz

Stroke = 2 m

# Solution -

Amplitude of the SHM will be half the stroke.

a = 2/2 = 1 m

Angular velocity is calculated by -

ω = 2πf

ω = 2 × 3.142 × 2

ω = 12.57 rad/s

Velocity of the piston at x = 0.75 m,

v = ω √(a^2-x^2)

v = 12.57 √(1^2-0.75^2)

v = 8.315 m/s

Acceleration of piston at x = 0.75 m,

acc = vω

acc = 8.315 × 12.57

acc = 104.5 m/s^2

Hope you understand..