A 28-g rifle bullet traveling 190 m/s embeds itself in a 3.1-kg pendulum hanging swing upward l an arc. Determine the vertical and horizonta

Question

A 28-g rifle bullet traveling 190 m/s embeds itself in a 3.1-kg pendulum hanging swing upward l an arc. Determine the vertical and horizontal components of the pendulum’s maximum displacement.

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Sapo 3 years 2021-07-25T20:12:07+00:00 1 Answers 18 views 0

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  1. quangkhai
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    2021-07-25T20:13:27+00:00
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    Answer:

    V = 0.15m

    H = 0.85m

    Explanation:

    We will be using the conservation of momentum to solve the problem.

    m(i).v(i) = m(f).v(f) where

    0.028 * 190 = 3.1 * v(f)

    v(f) = 5.32/3.1

    v(f) = 1.72 m/s

    next, we use the conservation of energy to find the vertical displacement.

    ½mv² = mgh

    ½v² = gh, making h the subject of formula, we have

    h = v²/2g

    h = 1.72²/ 2 * 9.81

    h = 2.9584 / 19.62

    h = 0.15 m

    The height, h is the vertical displacement.

    Next, we find the angle of the pendulum at the top of the swing.

    Φ = cos^-1 [(2.5 – 0.15)/2.5] *the height at which the pendulum is hanging is not given, so I assumed it to be 2.5m, yo can substitute that for whatever it is

    Φ = cos^-1(2.35/2.5)

    Φ = cos^-1 (0.94)

    Φ = 19.95°

    This gotten angle is used to find the horizontal displacement

    x = 2.5 sinΦ

    x = 2.5 sin 19.95

    x = 2.5 * 0.34

    x = 0.85 m

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