A solid aluminum ingot weighs 89 N in air. What is its volume? The ingot is suspended from a rope and totally immersed in water. What is the tension in the rope?

Answer 1

density of Al = 2.7*10^3 kg/m^3

weight = m g = 89 N
so
m = 89 N /9.8 m/s^2 = 9.08 kg

mass = density*volume
so
volume = mass/(2.7 *10^3)
so
volume = 9.08 /(2.7*10^3) = 3.36*10^-3 m^3

density of water = 10^3 kg/m^3
buoyancy = volume * density of water * g
= 3.36*10^-3*10^3 * 9.8 = 33 Newtons

weight - buoyancy = tension = 89-33