The Earth’s radius is 6378.1 kilometers. A mad scientist has come up with the simultaneously awesome and terrifying plan to increase the spe

Question

The Earth’s radius is 6378.1 kilometers. A mad scientist has come up with the simultaneously awesome and terrifying plan to increase the speed of the Earth’s rotation until people at the Earth’s equator experience a centripetal (radial) acceleration with a magnitude equal to g (9.81 m/s2 ), eectively making them experience weightlessness. If the mad scientist succeeds in their dastardly plan, what would be the new period of the Earth’s rotation?

in progress 0
bonexptip 5 years 2021-07-27T01:20:02+00:00 2 Answers 41 views 0

Answers ( )

  1. taiduc
    0
    2021-07-27T01:21:24+00:00
    Reply

    Answer:

    The time period of Earth’s rotation would be 84.4 minutes

    Explanation:

    Given that,

    Centripetal acceleration = 9.81 m/s²

    Radius ,r = 6378.1 km

    Velocity, v

    Centripetal acceleration is

    a_c=\dfrac{v^2}{r}

    a_c=\dfrac{v^2}{r}\\\\\Rightarrow v=\sqrt{a_cr}\\\\\Rightarrow v=\sqrt{9.81\times 6378100}\\\\\Rightarrow v=7910.067\ m/s

    Time period is given by

    T=\dfrac{2\times \pi \times r}{v\times 60}\\\\ T=\dfrac{2\times \pi \times 6378.1\times 10^3}{7910.06706\times 60}\\\\ T=84.4\ minutes

    Hence, the time period of Earth’s rotation would be 84.4 minutes

  2. Maris
    0
    2021-07-27T01:21:32+00:00
    Reply

    Answer: T = 5068 s

    Explanation:

    Given

    Radius of the earth, r = 6378.1 km

    Centripetal acceleration, g = 9.81 m/s²

    Period of rotation, T = ?

    a = w²r, where

    a is the centripetal acceleration

    w is the angular velocity

    r is the radius

    9.81 = w² * 6378.1*10^3

    w² = 9.81 / 6378.1*10^3

    w² = 1.538*10^-6

    w = 1.24*10^-3 rad/s

    To get the period of the earth, we use the formula

    w = 2π / T, so that

    T = 2π / w

    T = (2 * 3.142) / 1.24*10^-3

    T = 6.284 / 1.24*10^-3

    T = 5067.74 s

    Therefore, the earth would rotate at a period of 5068 s or 1 hour and 24 minutes

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )