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21 April, 00:18

A 1.0-kg standard cart A collides with a 0.10-kg cart B. The x component of the velocity of cart A is + 0.70 m/s before the collision and + 0.50 m/s after the collision. Cart B is initially traveling toward cart A at 0.40 m/s, and after the collision the x component of its velocity is + 1.6 m/s.

Part A: What is the x component of the change in the momentum of A?

Part B: What is the x component of the change in the momentum of B?

Part C: What is the sum of these two x components of the changes in momentum?

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Answers (1)
  1. 21 April, 00:31
    0
    Part A

    -0.2kgm/s

    Part B

    +0.12m/s

    Part C

    -0.08kgm/s

    Explanation

    Momentum of a body is defined as the product of mass of the body band its velocity.

    Momentum = mass * velocity

    Change in momentum = m (v-u)

    v is the final velocity of the body

    u is the initial velocity of the body.

    For cart A:

    Mass m = 1.0kg

    Initial velocity u = + 0.70m/s (velocity before collision)

    Final velocity' v = + 0.5m/s (velocity after collision)

    ∆Momentum = 1 (0.5-0.7)

    = 1 (-0.2)

    = - 0.2kgm/s

    The x component of the change in the momentum of A is - 0.2kgm/s

    For cart B:

    Similarly;

    ∆momentum = 0.1 (1.6-0.4)

    ∆momentum = 0.1*1.2

    ∆momentum = + 0.12kgm/s

    The x component of the change in the momentum of B is + 0.12kgm/s

    Part C:

    The sum of these two x components of the changes in momentum = (∆momentum) A + (∆momentum) B

    = - 0.2+0.12

    = - 0.08kgm/s
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