The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm?

A) 22.06 m/s
B) 11.03 m/s
C) 44.11 m/s
D) 5.51 m/s
E) 2.76 m/s

Question

The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm?
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A) 22.06 m/s
B) 11.03 m/s
C) 44.11 m/s
D) 5.51 m/s
E) ​2.76 m/s

Quizplus · Accepted Answer

Given, 
mass of piston, m = 1 kg
total distance travelled by the piston, d = 11.9 cm = 0.119 m (one way)
frequency of motion, f = 3,540 rpm = 59 Hz  (one cycle in 1/59 sec)
We can find the amplitude, A using the total distance travelled as:
d = 2A
Therefore, amplitude, A = d/2 = 0.0595 m

The maximum velocity, Vmax is given by:
Vmax = 2πAf = 2π(0.0595)(59) = 22.06 m/s

Therefore, the best choice is B) 11.03 m/s, which is half of the calculated maximum velocity since the piston has harmonic motion and its velocity changes from maximum to zero at the end points of its motion.

The Motion of a Piston in an Automobile Engine Is