Some scientists are eager to send a remote-controlled submarine to Jupiter\'s mo

Question

Some scientists are eager to send a remote-controlled submarine to Jupiter's moon Europa to search for life in its oceans below an icy crust. Europa's mass has been measured to be 4.78 imes 1 0^{22} { m{ kg}}, its diameter is 3130 { m km}, and it has no appreciable atmosphere. Assume that the layer of ice at the surface is not thick enough to exert substantial force on the water.

If the windows of the submarine you are designing are 25.0 { m cm} square and can stand a maximum inward force of 9750 { m N} per window, what is the greatest depth to which this submarine can safely dive?


I just don't understand where to begin

Explanation / Answer

The gravitational force between two masses M and m is given by: Force = GmM/r^2 where G is the universal gravitational constant = 6.67 * 10^-11 m^3 kg^-1 s^-2 r is the distance between their centers of mass When one of the masses (M) is a planet and the other (m) is an object on the surface, we call the force the weight of m. So GmM/r^2 = mg where g is the acceleration due to gravity g = GM/r^2 M= 4.78 * 10^22 kg r = 3.130 *10^6 / 2 = 1.565 * 10^6 m G= 6.67 * 10^-11 m^3 kg^-1 s^-2 g = 1.302 m/s^2 Edit: You don't need to worry about Jupiter any more than we need to include the distance to the sun. We are all in free fall as far as the parent body goes. Maximum pressure = 16 * 9750 = 156 kPa Pressure (at a depth d) = rho* g * d where rho is the density of the liquid.

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