7. A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original spe

Question

7. A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. What is the mass of the second ball

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Latifah 3 years 2021-08-25T04:43:06+00:00 1 Answers 4 views 0

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    2021-08-25T04:44:10+00:00

    Answer:

    mass of the second ball is 0.379m

    Explanation:

    Given;

    mass of first ball = m

    let initial velocity of first ball = u₁

    let final velocity of first ball  = v₁ = 0.45u₁

    let the mass of the second ball = m₂

    initial velocity of the second ball, u₂ = 0

    let the final velocity of the second ball = v₂

    Apply the principle of conservation of linear momentum;

    mu₁ + m₂u₂ = mv₁ + m₂v₂

    mu₁  +  0  = 0.45u₁m + m₂v₂

    mu₁  = 0.45u₁m + m₂v₂ ——– equation (i)

    Velocity for elastic collision in one dimension;

    u₁ + v₁ = u₂ + v₂

    u₁ + 0.45u₁ = 0 + v₂

    1.45u₁ = v₂ (final velocity of the second ball)

    Substitute in v₂ into equation (i)

    mu₁  = 0.45u₁m + m₂(1.45u₁)

    mu₁ = 0.45u₁m + 1.45m₂u₁

    mu₁ – 0.45u₁m = 1.45m₂u₁

    0.55mu₁ = 1.45m₂u₁

    divide both sides by u₁

    0.55m = 1.45m₂

    m₂ = 0.55m / 1.45

    m₂ = 0.379m

    Therefore, mass of the second ball is 0.379m (where m is mass of the first ball)

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