1 Calculate the buoyancy force acting on a floating cube tha

1. Calculate the buoyancy force acting on a floating cube that is 75% submerged. The cube has side lengths of 20 cm.

2. A small boat has rough dimensions of 8 meters long by 5 meters wide with a mass of 6000 kg. Approximating the boat as a rectangular prism, calculate the water line on the boat.

3. Define Bernoulli’s Principle

Solution

1) Volume of Cube = 20^3   = 8000 cm^3

     Volume of Cube submerged   = 0.75 * 20^3   = 6000 cm^3

     Buoyancy Force   = rho_water * V_submerged * g    = 1000 * 6000 * 10^-6 * 9.8   = 58.8 N

2) Buoyancy Force = Weight of boat

     rho_water * V_submerged * g   = 6000 * 9.8

     1000 * V_submerged = 6000

     V_submerged   = 5 * 8 * x    = 6000 / 1000

     x = 0.15 m height is submerged in water

3) Bernoulli\'s principle states that for an inviscid flow of a nonconducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid\'s potential energy.