A 10.0 kg and a 2.0 kg cart approach each other on a horizontal frictionless air track. Their total kinetic energy before collision is 96 J.

Question

A 10.0 kg and a 2.0 kg cart approach each other on a horizontal frictionless air track. Their total kinetic energy before collision is 96 J. Assume their collision is elastic. What is the final speed in m/s of the 10.0 kg mass if that of the 2.0 kg mass is 8.0 m/s? (Hint: There are 2 conditions for elastic collisions.)

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Nick 4 years 2021-07-22T10:57:19+00:00 1 Answers 15 views 0

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  1. Bo
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    2021-07-22T10:58:52+00:00
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    Answer:

    2.53 m/s

    Explanation:

    From the law of conservation of momentum,

    For an Elastic collision,

    Total kinetic energy before collision = Total kinetic energy after collision

    Ek₁ = 1/2mv²+1/2m’v’²…………….. Equation 1

    Where Ek₁ = total kinetic energy before collision, m = mass of the first cart, v = final velocity of the first cart, m’ = mass of the second cart, v’ = final velocity of the second cart.

    Given: Ek₁ = 96 J, m = 10 kg, m’ = 2 kg, v’ = 8 m/s.

    Substitute into equation 1 and solve for the value of v.

    96 = 1/2(10)(v²)+1/2(2)(8²)

    96 = 5v²+64

    5v² = 96-64

    5v² = 32

    v² = 32/5

    v² = 6.4

    v = √6.4

    v = 2.53 m/s

    Hence the final speed of the 10 kg mass = 2.53 m/s

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