A 7.7 kg sphere makes a perfectly inelastic collision with a second sphere initially at rest. The composite system moves with a speed equal

Question

A 7.7 kg sphere makes a perfectly inelastic collision with a second sphere initially at rest. The composite system moves with a speed equal to one third the original speed of the 7.7 kg sphere. What is the mass of the second sphere

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Thành Đạt 2 months 2021-07-31T08:23:00+00:00 2 Answers 1 views 0

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    0
    2021-07-31T08:24:39+00:00

    Answer:

    The mass of the second sphere is 15.4 kg

    Explanation:

    Given;

    mass of the first sphere, m₁ = 7.7 kg

    initial velocity of the second sphere, u₂ = 0

    let mass of the second sphere =  m₂

    let the initial velocity of the first sphere = u₁

    final velocity of the composite system, v = ¹/₃ x u₁ = \frac{u_1}{3}

    From the principle of conservation of linear momentum;

    Total momentum before collision = Total momentum after collision

    m₁u₁ + m₂u₂ = v(m₁ + m₂)

    Substitute the given values;

    7.7u_1 + 0=\frac{u_1}{3} (7.7+m_2)

    Divide through by u₁

    7.7 = ¹/₃(7.7 + m₂)

    multiply both sides by 3

    23.1 = 7.7 + m₂

    m₂ = 23.1 – 7.7

    m₂ = 15.4 kg

    Therefore, the mass of the second sphere is 15.4 kg

    0
    2021-07-31T08:24:54+00:00

    Answer:

    15.4 kg.

    Explanation:

    From the law of conservation of momentum,

    Total momentum before collision = Total momentum after collision

    mu+m’u’ = V(m+m’)……………….. Equation 1

    Where m = mass of the first sphere, m’ = mass of the second sphere, u = initial velocity of the first sphere, u’ = initial velocity of the second sphere, V = common velocity of both sphere.

    Given: m = 7.7 kg, u’ = 0 m/s (at rest)

    Let: u = x m/s, and V = 1/3x m/s

    Substitute into equation 1

    7.7(x)+m'(0) = 1/3x(7.7+m’)

    7.7x = 1/3x(7.7+m’)

    7.7 = 1/3(7.7+m’)

    23.1 = 7.7+m’

    m’ = 23.1-7.7

    m’ = 15.4 kg.

    Hence the mass of the second sphere = 15.4 kg

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