1) Calculate the torque required to accelerate the Earth in 5 days from rest to its present angular speed about its axis. 2) Calculate the

Question

1) Calculate the torque required to accelerate the Earth in 5 days from rest to its present angular speed about its axis. 2) Calculate the energy required. 3) Calculate the average power required.

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Minh Khuê 1 year 2021-09-03T19:19:12+00:00 1 Answers 49 views 0

Answers ( )

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    2021-09-03T19:20:32+00:00

    Answer:

    a) τ = 4.47746 * 10^25 N-m

    b) E = 2.06301 * 10^13 J

    c) P = 3.25511*10^21 W

    Explanation:

    Given that,

    The radius of earth r = 6.3781×10^6 m

    The angular speed of earth w = 7.27*10^-5 rad/s

    The time taken to reach above speed t = 5 yrs = 1.57784760 * 10^8 s

    The mass of earth m = 5.972 × 10^24 kg

    The inertia of sphere I = 2/5 * m* r^2

    Solution:

    angular acceleration of the earth from rest to w is given by α:

                                   α = w / t

                                   α = (7.27*10^-5) / (1.57784760 * 10^8)

                                   α = 4.60754*10^-13 rad/s^2

    The required torque τ is given by:

                                   τ = I*α

                                   τ = 2/5 * m* r^2 * α

     τ = 2/5 *(5.972 × 10^24) * (6.3781×10^6)^2 * (4.60754*10^-13)

     τ = 4.47746 * 10^25 N-m

    Power required P to turn the earth to the speed w is:

                              P = τ*w

                              P = (4.47746 * 10^25)*(7.27*10^-5)

                              P = 3.25511*10^21 W

    Energy E required is :

                              E = P / t

                              E = (3.25511*10^21) / (1.57784760 * 10^8)

                              E = 2.06301 * 10^13 J

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