As shown in the figure below, a bullet of mass m-0.1 kg and speed D passes compl

Question

As shown in the figure below, a bullet of mass m-0.1 kg and speed D passes completely through a pendulum bob of mass m-2kg. The bullet emerges with a speed of 100m/s. The pendulum bob is suspended by a stiff rod of length t = 50 cm, and negligible mass. Assuming that the velocity of the bullet was 200m/s, what is the velocity of the bob just after the bullet passes through it. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? Now suppose the original speed of the bullet was 350m/s, what would be the tension the rod, just as it reaches the highest point?

Explanation / Answer

initial speed of bob=0 m/s

let final speed be u m/s

initial speed of bullet = 200 m/s

final speed of bullet=100m/s

by conservation of linear momentum

initial momentum of system =final momentum of system

200*0.1=0.1*100+(2*u)

u=5 m/s

(b) the bob will complete circle if bob reaches the top.

let the speed of bob at bottom be x m/s so that it reaches top .

by conservation of energy we get

0.5*2*x^2=2*9.8*1

x=4.42 m/

now we have to find v such that final speed of bob be 4.42 m/s

0.1*v=0.1*100+(2*4.42)

we get v=188.4 m/s

(c)The rod does not have any tension .It will have normal force as follows

if speed of bullet is 350m/s

we get final speed ob bob to be 12.5 m/s

by conservation of energy

0.5*2*(velocity at top)^2+2*9.8*1=0.5*2*12.5^2

velocity at top=11.68 m/s

normal at top=(2*11.68^2/0.5)-(2*9.8)=527 N

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