A barge floating in fresh water (rho = 1000 kg/m3) is shaped like a hollow rectangular prism with base area A = 550 m2 and heigh
t H = 2.0 m. When empty the bottom of the barge is located H0 = 0.45 m below the surface of the water. When fully loaded with coal the bottom of the barge is located H1 = 1.4 m below the surface.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.c) Find the mass of the coal in terms of the given data.d) Find the mass of the coal in kilograms.e) How far would the barge be submerged (in meters) if mc,2 = 250000 kg of coal had been placed in the empty barge?
Given there are three blocks of masses , and (ref image in attachment)
When all three masses move together at an acceleration a, the force F is given by
F = ( + + ) *a ................(equation 1)
Also it is given that does not move with respect to , which gives tension T is exerted on pulley by only, Hence tension T is
T = *a ..........(equation 2)
There is also also tension exerted by . There are two components here: horizontal due to acceleration a and vertical component due to gravity g. Thus tension is given by
T = ................(equation 3)
From equation 2 and 3, we get
*a =
Squaring both sides we get
* = * (+)
* = ( * )+ ( *)
( - ) * = *
= */( - )
Taking square root on both sides, we get acceleration a
a = *g/()
Hence substituting the value of a in equation 1, we get