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16 September, 02:45

A 12.0 g bullet was fired horizontally into a 1 kg block of wood. The bullet initially had a speed of 250 m/s. The block of wood was hanging from a 2 m long piece of (massless) string. After the collision the block/bullet combined object swings upward on the string. Find the height the block/bullet combined object rises.

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Answers (2)
  1. 16 September, 03:28
    0
    0.45 m

    Explanation:

    From the law of conservation of momentum,

    mv = (m + M) V where m = mass of bullet = 12 g = 0.012 kg, v = initial speed of bullet = 250 m/s, M = mass of block = 1 kg, V = final velocity of bullet and block.

    V = mv / (m + M) = 0.012 kg 250 m/s / (0.012 + 1) kg = 3/1.012 = 2.96 m/s

    From the law of conservation of energy,

    ΔU + ΔK = 0 where U = potential energy of mass and block and K = kinetic energy of mass and block

    ΔU = - ΔK

    (m + M) gh - 0 = - [0 - 1/2 (m + M) V²]

    (m + M) gh - 0 = - [0 - 1/2 (m + M) V²]

    (m + M) gh = 1/2 (m + M) V²

    gh = 1/2V²

    h = V²/2g where h is the height moved by the combined bullet and block

    h = (2.96 m/s) ² / (2 * 9.8 m/s²)

    h = 0.45 m
  2. 16 September, 06:04
    0
    The rise in height of combined block/bullet from its original position is 0.45m

    Explanation:

    Given;

    mass of bullet, m₁ = 12 g = 0.012 kg

    mass of block of wood, m₂ = 1 kg

    initial speed of bullet, u₁ = 250 m/s.

    initial speed of block of wood, u₂ = 0

    From the principle of conservation of linear momentum, calculate the final speed of the combined block/bullet system.

    m₁u₁ + m₂u₂ = v (m₁+m₂)

    where;

    v is the final speed of the combined block/bullet system.

    0.012 x 250 + 0 = v (0.012 + 1)

    3 = v (1.012)

    v = 3/1.012

    v = 2.96 m/s

    From the principle of conservation of energy, calculate the rise in height of the block/bullet combined from its original position.

    ¹/₂mv² = mgh

    ¹/₂v² = gh

    ¹/₂ (2.96) ² = (9.8) h

    4.3808 = 9.8h

    h = 4.3808/9.8

    h = 0.45 m

    Therefore, the rise in height of combined block/bullet from its original position is 0.45m
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