Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary.

Question

Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary.

A. If the collision is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2?

Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v.

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Thái Dương 6 months 2021-08-19T19:08:28+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-19T19:10:26+00:00

    Answer:

    (v, 0) or (0, v)

    Explanation:

    The law of conservation of linear momentum states total initial momentum equal total final momentum.

    Total initial momentum = mv + m\times 0 = mv

    Total final momentum = mv_1 + mv_2 = m(v_1+v_2)

    Equating both,

    mv = m(v_1+v_2)

    v = v_1+v_2

    For an elastic collision, kinetic energy is conserved i.e. total initial kinetic energy = total final kinetic energy

    \frac{1}{2}mv^2 + \frac{1}{2}m\times0^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2

    v^2 = v_1^2+v_2^2

    From the first equation, v_1 = v-v_2.

    Substituting this in the second equation,

    v^2 = (v-v_2)^2+v_2^2

    v^2 = v^2-2vv_2 +v_2^2+v_2^2

    0 = 2v_2^2-2vv_2

    v_2(v_2-v) = 0

    v_2 = 0 or v_2 = v

    From v_1 = v-v_2,

    v_1 = v-v = 0

    OR

    v_1 = v-0 = v

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