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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Khánh Gia 5 years 2021-09-03T19:21:33+00:00 1 Answers 19 views 0

Answers ( )

  1. Dulcie
    0
    2021-09-03T19:23:17+00:00
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    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:

    – 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:

    – The 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

    – The 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

    – The 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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