Engineers are designing a digital scale for use on Titan, Saturn’s largest moon, where the local gravitational field strength is 1.36N/kg. To validate the scale, they use a cylindrical storage tank that will be completely filled with liquid methane.
(a) The empty tank has a uniform inner radius of 0.30m, an inner height of 0.80m, and an empty mass of 50kg. The density of liquid methane is 450kg/m3. Calculate the mass of liquid methane required to fill the tank to the brim.
(b) Determine the total gravitational force that Titan exerts on the combined tank–methane system when the tank is fully filled.
(c) After calibration, the filled tank is transported to Earth. Without re-measuring any masses, predict the reading that an ideal (frictionless, properly calibrated) digital scale would display for the same filled tank at Earth’s surface, where g=9.8N/kg. Explain the reasoning that leads to your prediction.