A 2.0 kg sphere with a velocity of 6.0 m/s collides head-on and elastically with a stationary 10 kg sphere

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A 2.0 kg sphere with a velocity of 6.0 m/s collides head-on and elastically with a stationary 10 kg sphere

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Xavia 5 months 2021-08-31T06:48:23+00:00 1 Answers 7 views 0

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    2021-08-31T06:49:29+00:00

    Question: A 2.0 kg sphere with a velocity of 6.0 m/s collides head-on and elastically with a stationary 10 kg sphere, What is thier velocities after collision.

    Answer:

    v = 6 m/s, v’ = 0 m/s

    Explanation:

    From the question,

    For Elastic collision,

    mu+m’u’ = mv+m’v’……………………. Equation 1

    Where m = mass of the first sphere, m’ = mass of the second sphere, u = initial velocity of the first sphere, u’ = initial velocity of the second sphere, v = final veolocity of the first sphere, v’ = final velocity of the second sphere.

    Also,

    The relative velocity before collision = relative velocity after collision

    u-u’ = v-v’………………………. Equation 2

    Given:  m = 2 kg, m’ = 10 kg, u = 6 m/s, u’ = 0 m/s

    Substitute into equation 1 and 2

    2(6)+10(0) = 2v+10v’

    2v+10v’ = 12………….. Equation 3

    6-0 = v-v’

    v-v’ = 6 ………………. Equation 4

    Solve equation 3 and 4 simultaneously.

    v = 6+v’…………. Equation 5

    Substitute equation 5 into equation 3

    2(6+v’)+10v’ = 12

    12+2v’+10v’ = 12

    12v’ = 12-12

    v’ = 0/12

    v’ = 0 m/s.

    Also substitute the value of v’ into equation 5

    v = 6+0

    v = 6 m/s

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