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 4.78x10^22 kg, its diameter is 3130 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.

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


I dont understand how solve this problem seems easy, but cant seem to get it. please be detailed if possible

Explanation / Answer

First you must find the total pressure exerted on the window in Pa (N/m^2). So 9750/(0.25^2) = 156000 Pa = total pressure each window can withstand. Now use gravitation formula g = GM/R^2 to get gravity. G = 6.67*10^-11, and R = (3130/2)*1000(radius not diameter and must be in meters). So g = (6.67*10^-11)(4.78*10^22)/(1.565*10^6), and g = 1.30 m/s^2. Now use formula P=(rho)gh to solve for h, no other pressures are taken into account because the pressure inside the submarine should be zero because of Europa's lack of atmosphere, and the crust doesn't affect the water pressure. 156000 = 1000*1.30*h ----> h = 119.8m

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