n deep space, sphere A of mass 47 kg is located at the origin of an x axis and sphere B of mass 110 kg is located on the axis at x = 3.4 m.

Question

n deep space, sphere A of mass 47 kg is located at the origin of an x axis and sphere B of mass 110 kg is located on the axis at x = 3.4 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 2.6 m toward A?

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Thu Nguyệt 5 years 2021-07-20T19:04:52+00:00 1 Answers 22 views 0

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  1. Helga
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    2021-07-20T19:06:38+00:00
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    Answer:

    a)-1.014x 10^{-7J

    b)3.296 x  10^{-7J

    Explanation:

    For Sphere A:

    mass ‘Ma’= 47kg

    xa= 0

    For sphere B:

    mass ‘Mb’= 110kg

    xb=3.4m

    a)the gravitational potential energy is given by

    U_{i = -GMaMb/ d

    U_{i= – 6.67 x 10^{-11} x 47 x 110/ 3.4 => -1.014x 10^{-7J

    b) at d= 0.8m (3.4-2.6) and U_{i=-1.014x 10^{-7J

    The sum of potential and kinetic energies must be conserved as the energy is conserved.

    K_{i + U_{i= K_{f + U_{f

    As sphere starts from rest and sphere A is fixed at its place, therefore K_{i is zero

    U_{i= K_{f + U_{f

    The final potential energy is

    U_{f= – GMaMb/d

    Solving for ‘K_{f ‘

    K_{f = U_{i + GMaMb/d => -1.014x 10^{-7 + 6.67 x 10^{-11} x 47 x 110/ 0.8

    K_{f = 3.296 x  10^{-7J

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