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28 August, 15:17

n explosion breaks an object initially at rest into two pieces, one of which has 2.0 times the mass of the other. If 8400 J of kinetic energy were released in the explosion, how much kinetic energy did the heavier piece acquire

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  1. 28 August, 17:13
    0
    The heavier piece acquired 2800 J kinetic energy

    Explanation:

    From the principle of conservation of linear momentum:

    0 = M₁v₁ - M₂v₂

    M₁v₁ = M₂v₂

    let the second piece be the heavier mass, then

    M₁v₁ = (2M₁) v₂

    v₁ = 2v₂ and v₂ = ¹/₂ v₁

    From the principle of conservation of kinetic energy:

    ¹/₂ K. E₁ + ¹/₂ K. E₂ = 8400 J

    ¹/₂ M₁ (v₁) ² + ¹/₂ (2M₁) (¹/₂v₁) ² = 8400

    ¹/₂ M₁ (v₁) ² + ¹/₄M₁ (v₁) ² = 8400

    K. E₁ + ¹/₂K. E₁ = 8400

    Now, we determine K. E₁ and note that K. E₂ = ¹/₂K. E₁

    1.5 K. E₁ = 8400

    K. E₁ = 8400/1.5

    K. E₁ = 5600 J

    K. E₂ = ¹/₂K. E₁ = 0.5*5600 J = 2800 J

    Therefore, the heavier piece acquired 2800 J kinetic energy
  2. 28 August, 18:41
    0
    The heavier piece acquired 2800J of energy.

    Explanation:

    Let the velocity of the first piece be v1 and that of the second piece be v1 and also let the masses be m1 and m2 respectively.

    m2 = 2m1

    From the principles of conservation of momentum

    m1v1 = m2v2

    m1v1 = 2m1v2

    Dividing through by m1

    That is v1 = 2v2

    v2 = 1/2v1

    Total kinetic energy = 8400J

    1/2m1v1² + 1/2m2v2² = 8400

    1/2m1v1² + 1/2 (2m1) * (1/2v1) ² = 8400

    1/2m1v1² + 1/4m1v1² = 8400

    Let 1/2m1v1 = K1

    K1 + 1/2K1 = 8400

    3/2K1 = 8400

    K1 = 8400 * 2/3 = 5600J

    K2 = 8400 - 5600 = 2800J
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