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7 June, 04:02

A 144-g baseball moving 27 m/s strikes a stationary 5.25-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at 1.07 m/s.

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  1. 7 June, 04:29
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    A. - 12.01 m/s

    B. Kinetic energy before collision = 52.488 J

    Kinetic energy after collision = 13.40 J

    Explanation:

    Parameters given:

    Mass of ball = 144g = 0.144kg

    Initial velocity of ball = 27 m/s

    Mass of brick = 5.25kg

    Initial velocity of brick = 0 m/s

    Final velocity of brick = 1.07m/s

    A. To find the Final velocity of the ball, we use the law of conservation of momentum i. e.

    Total initial momentum = Total final momentum

    Initial momentum of ball = m*u

    = 0.144 * 27

    = 3.888 kgm/s

    Initial momentum of brick = m*u

    = 5.25 * 0

    = 0 kgm/s

    Total initial momentum = 3.888 + 0

    = 3.888 kgm/s

    Final momentum of ball = 0.144 * v

    = 0.144v

    Final momentum of brick = 5.25 * 1.07

    = 5.6175 kgm/s

    Total final momentum = 0.144v + 5.6175

    Hence,

    3.888 = 0.144v + 5.6175

    => 0.144v = 3.888 - 5 6175

    0.144v = - 1.7295

    v = - 1.7295/0.144

    v = - 12.01m/s

    Therefore, the final velocity of the ball is - 12.01m/s. The negative sign indicates that it's moving opposite to the initial velocity.

    B. Kinetic energy of ball before collision =

    0.5 * m * u^2

    = 0.5 * 0.144 * 27^2

    = 52.488 J

    Kinetic energy of the brick before collision =

    0.5 * 5.25 * 0

    = 0 J

    Total kinetic energy before collision is:

    52.488 + 0 = 52.488 J

    Kinetic energy of ball after collision

    = 0.5 * 0.144 * (12.01) ^2

    = 10.39J

    Kinetic energy of brick after collision

    = 0.5 * 5.25 * 1.07^2

    = 3.01 J

    Total kinetic energy after collision

    = 10.39 + 3.01

    = 13.40 J
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