Submarines on Europa. 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 4.8 × 1022 kg, its diameter is 3138 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 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?
Step 1: 22 Mass of Europa M = 4.8 x 10 kg Diameter D = 3138 km Radius of Europa R = 1569 km or 1.57 x 10 m 6 Length of the window L = 25 cm or 0.25 m Maximum inward force per window F = 9750 N Gravitational constant G = 6.67 x 10 -11N m /kg2 Step 2: To find the greatest depth to which this submarine can safely dive Atmosphere on the surface of Europa is not appreciable. Hence atmospheric pressure on the surface P 0s zero. Assume that the submarine penetrates the icy layer and goes below its ocean. Pressure under water can be felt. Pressure under the ocean is given by P = hg h = P -----(1) g Where h is the depth to be calculated g - acceleration due to gravity on Europa - density of water under icy crust (1000 kg/m ) 3 Step 3: Calculating acceleration due to gravity g = GM R 2 6.67*101* 4.* 1022 g = 62 (1.5* 10 ) g = 1.299 m/s ------(2)