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31 July, 20:08

An 30 g rifle bullet traveling at 390 m/s buries itself in a 4 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the maximum vertical displacement of the pendulum (height). (g

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  1. 31 July, 22:09
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    Mass of bullet 30g=30/1000=0.03kg

    Speed of bullet = 390m/s

    Mass of pendulum is 4kg

    Total mass of bullet and pendulum, = 4.03kg

    Length of pendulum is L = 2.8m

    Then, momentum is conserved

    Momentum before collision = momentum after Collision

    Mass of bullet * Velocity of bullet=combine mass of bullet and pendulum * velocity of pendulum

    0.03*390=4.03*V

    V=0.03*390/4.03

    V=2.9m/s

    Then the Kinetic energy of pendulum is given as

    K. E=½mv²

    K. E=½*4.03*2.9²

    K. E=16.95J

    conservation of energy states that energy can neither be created nor destroy but can be transferred from one form to another.

    Let acceleration due to gravity be

    g=9.81m/s²

    The vertical displacement of the pendulum (h) = ?

    Potential energy of the pendulum is given as

    P. E=mgh

    P. E=4.03*9.81*h

    P. E=39.53h

    So the P. E of the pendulum equals K. E of the pendulum

    P. E=K. E

    39.53h=16.95

    h=16.95/39.53

    h=0.43m

    Knowing the height we can find the angle of the pendulum at the top of the swing:

    θ=arcos (l-h) / l

    θ=arcos (2.8-0.43) / 2.8

    θ=arcos (0.8464)

    θ=32.2°

    From A we get the displacement along the horizontal axis:

    The maximum vertical displacement is

    x=h Sinθ

    x=0.43 Sin32.2

    x=0.23m

    So the displacement are (0.23,0.43) m
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