The motion of the piston of an automobile engine (See the figure (Figure 1) ) is

Question

The motion of the piston of an automobile engine (See the figure (Figure 1) ) is approximately simple harmonic.

Mass = 0.500 KG

If the engine runs at 7000 rev/min, what net force must be exerted on it at the endpoint of its stroke? The motion of the piston of an automobile engine (See the figure (Figure 1)) is approximately simple harmonic Submit My Answers Give Up Part G If the engine runs at 7000 rev/min , what is the speed of the piston at the midpoint of its stroke? u= m/s Submit My Answers Give Up Part H If the engine runs at 7000 rev/min, what is the kinetic energy of the piston at the midpoint of its stroke? Figure 1 Submit My Answers Give Up 0.100 m Part I If the engine runs at 7000 rev/min , what average power is required to accelerate the piston from rest to the speed found in part G?

Explanation / Answer

Part f) frequency, f=7000rev/min=7000/60 rev per sec

time period, T=1/f= 6/700 sec

also, T = 2 (m/k)

6/700=2*(22/7)*(0.5/k)

6/4400 =(0.5/k)

0.5/k=1.86*10-6

k=2.68889*105N/m

force=kx= 2.7*105 N/m* 0.05m (because x is the distance of piston from mid position to extreme position=0.100/2)

force=13444N

Part G)for finding speed, lets equate energy

Kinetic Energy at mid position= spring Potential Energy at end position

0.5 mv2=0.5kx2

v2=2.7*105 x2/0.5 =540000 x2

v=735x =735*0.05=36.8 m/s

Part H)kinetic energy = 0.5mv2= 0.5*0.5*36.82= 338.5J

Part I) Power = work done/time taken

= 338.5/((6/700)/4 (Here we have divided by because time taken from mean position to extreme is T/4)

=338.5*2800/6

=157966 W

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