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14 November, 13:40

Two carts with masses of 4.2 kg and 3.2 kg move toward each other on a frictionless track with speeds of 5.4 m/s and 4.5 m/s, respectively. The carts stick together after colliding head-on. Find their final speed. Answer in units of m/s.

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  1. 14 November, 17:37
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    Answer:the final speed is 5.01 m/s

    Explanation:

    Momentum is the product of mass and velocity.

    Cart 1 has a mass of 4.2kg and a speed 5.4 m/s

    Cart 2 has a mass of 3.2kg and a speed 4.5 m/s

    Total momentum before collision is

    m1u1 + m2u2. It becomes

    4.2*5.4 + 3.2*4.5 = 22.68 + 14.4

    = 37.08kgm/s

    The carts stick together after colliding head-on. This means that they move with a common velocity, v. Therefore, Total momentum after collision is (m1 + m2) v. It becomes

    (4.2 + 3.2) v = 7.4v

    According the the law of conservation of momentum, the total momentum before collision = the total momentum after collision. Therefore,

    7.4v = 37.08

    v = 37.08/7.4 = 5.01 m/s
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