Yahoo 知識+ 將於 2021 年 5 月 4 日 (美國東岸時間) 停止服務,而 Yahoo 知識+ 網站現已轉為僅限瀏覽模式。其他 Yahoo 資產或服務,或你的 Yahoo 帳戶將不會有任何變更。你可以在此服務中心網頁進一步了解 Yahoo 知識+ 停止服務的事宜,以及了解如何下載你的資料。

Al P
Lv 7
Al P 發問於 Science & MathematicsPhysics · 1 十年前

Easy fluid mechanics problem?

The planet mercury has been turned into mercury with the

uniform denstiy (p) of liquid mercury. An alien pentagonal

obelisk (density=p/3) containing a message for earth remains

at rest near mercury's center until equilibrium is reached at which

time it moves along the radial coordinate without frictional head.

In order to reach Earth, the oblisk must reach escape velocity.

Does the obelisk reach Earth?

Data planet

No thermo.

elastic modulus = 3 * 10 ^ 9 N/m^2

p = 13570 kg/m^3

Data obelisk:

h1 = 10m (body)

h2 = 1m

edge=1 m

更新:

Hydrostatics

更新 2:

Please express your answer numerically.

The data is there for a reason.

2 個解答

相關度
  • 匿名
    1 十年前
    最愛解答

    The PE to escape from the planet's surface is

    PE1 = - mMG/R

    Assuming constant density from the surface to the center, the gravitational field varies with

    F = m MG/R^2 * r/R

    or integrating from 0 to R

    PE2 = ∫ m MG/R^2 * r/R dr [From R to 0]

    PE2 = m MG/R^2 1/2 r^2/R [From R to 0]

    PE2 = m -1/2 MG/R

    However, Archemides rules and, at least until the obelisk reaches the surface, you will have a net bouyance of - 2/3 m. (This is just the PE of the mercury moving towards the center and displacing the obelisk up)

    So, we just combine everything and see where we are:

    Σ PE = - mMG/R + 2/3 m *1/2 MG/R

    Σ PE = - 2/3m MG/R

    It will only have 1/3 of the energy it needs to escape or a velocity at the surface of v = √1/3 v.esc. Actually, it wouldn't even have enough energy to reach orbit which is v.orbit = √ 1/2 v.esc.

  • 匿名
    1 十年前

    Easy my @rse.

還有問題嗎?立即提問即可得到解答。