Posted by **Katie** on Friday, July 9, 2010 at 4:38pm.

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 10.0 cm, what is its maximum speed when the engine is running at 3 000 rpm? The answer is 15.7 m/s but I don't understand how to get there.

- Physics -
**bobpursley**, Friday, July 9, 2010 at 4:45pm
displacement=Amax(SIN W T)

VELOCITY= aMAX*W*COS WT

MAX VELOCITY=AMAX*W=.05M*2pi*3000RAD/60

MAX VELOCITY=.05*2pi*50

- Physics -
**drwls**, Friday, July 9, 2010 at 4:47pm
Maximum speed is w A, where w is the angular velocity and A is the amplitude. The amplitude A is half the displacement of the engine, or 5.0 cm.

The angular velocity in your case is

w = (3000 rev/min)*(2 pi rad/rev)/(60 sec/min) = 314 rad/s

Vmax = 5.0*314 = 1570 cm/s = 15.7 m/s

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