A bullet of mass m=26g is fired into a wooden block of mass M=4.7kg. The block is attached to a string of length 1.5m. The bullet is embedde

Question

A bullet of mass m=26g is fired into a wooden block of mass M=4.7kg. The block is attached to a string of length 1.5m. The bullet is embedded in the block, causing the block to then swing. If the block reaches a maximum height of h=0.31m, what was the initial speed of the bullet?

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Hải Đăng 5 years 2021-07-29T07:17:03+00:00 1 Answers 30 views 0

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  1. Dulcie
    0
    2021-07-29T07:18:48+00:00
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    Answer:

    u = 449 m/s

    Explanation:

    Given,

    Mass of the bullet, m = 26 g

    Mass of the wooden block,M = 4.7 Kg

    height of the block,h = 0.31 m

    initial speed of the block, u = ?

    Using conservation of energy

    (M+ m)gh = \dfrac{1}{2}(M+m)v^2

    gh = \dfrac{1}{2}v^2

    v=\sqrt{2gh}

    v=\sqrt{2\times 9.81\times 0.31}

    v = 2.47 m/s

    Now, using conservation of momentum to calculate the speed of the bullet.

    m u + M u’ = (M+m)v

    m u  = (M+m)v

    0.026 x u  = (4.7+0.026) x 2.47

    u = 449 m/s

    Hence, the speed of the bullet is equal to 449 m/s.

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