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A barge floating in fresh water (rho = 1000 kg/m3) is shaped like a hollow rectangular prism with base area A = 550 m2 and height 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 = 1.8 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?

Respuesta :

Answer:

Explanation:

volume of barge = 1/3 A H

=1/3 x 550 x 2

= 366.67 m³

When empty the bottom of the barge is located H0 = 0.45 m below the surface of the water ,

volume above  water = A /12 x ( H - H₀ )³

= 170 m³

volume below   water = 366.67 -170 = 96.66 m³

Buoynant force = weight of displaced water

= 96.66x 10³x 9.8

=947.26 x 10³ N

= weight of empty  barge

mass of empty  barge = 96.66 x 10³kg

When fully loaded with coal the bottom of the barge is located H1 = 1.8 m below the surface

volume above  water = A /12 x ( H - H₁ )³

volume below   water = (A/3) H - A /12 x ( H - H₁ )³

BUOYANT FORCE = Weight of water displaced

= ρg[(A/3) H - A /12 x ( H - H₁ )³ ]

Substituting the values

Buoyant force = [366.67  - 550 / 12 x ( 2-1.8 )³]x 10³ x 9.8

= 3589.77 x 10³ N

WEIGHT OF COAL = 3589.77 x 10³  - 947.26 x 10³

= 2642.51 x 10³N

MASS OF THE COAL = 2642.51 x 10³ / 9.8

= 269.64 x 10³ kg

jayilych4real

The equation for the buoyant force on the empty is force= density * area * height

Calculations and Parameters:

Given that:

  • Density, P= 1000 kg/m^3
  • Area= 550m^2
  • Height= 2m
  • When empty, H0= 0.45m
  • Fully loaded, H1=. 1.8m

b. Mass of =?

But density= mass/volume

Mass= density * volume

Mass= 1000 * 550 * 2

Mass= 1.1 * 10^6kg.

c. Mass of coal=?

Height of barge when loaded with coal= 1

Density of barge, P= 1000kg/m^3

Area of barge, A= 550m^2

Density= Mass x gravity/volume

Mass= density x volume/gravity.

Mass= 1000 * 550 * 1.8

=9.9 * 10^5kg.

d. Mass of coal= 250000kg

Height of empty barge = 0.45m

Density = 550m^2

Distance =?

Mass = density * area * H0 * distance

250000/1000 * 550

=0.45d

d= 1m

Read more about distance here:

https://brainly.com/question/2854969

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