A barge floating in fresh water (rho = 1000 kg/m^3) is shaped like a hollow rectangular prism with base area A = 550 m^2 and height H = 2.0 m. When empty the bottom of the barge is located H0 = 0.55 m below the surface of the water. When fully loaded with coal the bottom of the barge is located H1 = 1.35 m below the surface.
Randomized Variables
A = 750 m²
H₀ = 0.55 m
Hᵢ = -1.1 m
(A) Write an equation for the buoyant force on the empty barge in terms of the known data.
(B) Determine the mass of the barge in kilograms.

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm