a ball point pen has a spring mechanism that allos the user to extend an retract

Question

a ball point pen has a spring mechanism that allos the user to extend an retract the ball point. assume the pen has a mass of 30 grams. suppose the spring mechanism is depressed the maximum amount (5mm) and the user lets go of the pen and it jumps 35mm into the air. (a) what is the max PE of the pen at the top of its flight (b) what was the pen initial speed upward just as it left the surface of the table (c) how long does it take the pen to reach the top of its trajectory and (d) what was the average power delivered to the pen ?

Explanation / Answer

PE max is at highest point=0.03*10*0.035 =0.0105 J

V2=2gh

V=0.83 m/s

t= V/g =0.083 sec

Pavg till it reaches top is 0.0105/0.083 = 0.12 watt

Pavg till it comes back = 0

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