Solve Archimedes Principle: 800kg Load on 5x2m Barge in Fresh Water

[jaisan72980]

Homework Statement

A rectangular barge, 5 meters long and 2 meters wide, floats in fresh water. How much deeper will the barge sink when a 800 kg load is added to the barge? Use a density of water of 1000 kg per cubic meter.

Homework Equations

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The Attempt at a Solution

completely lost

 

[ehild]

What do you know about Archimedes' Principle?

 

[kerimek]

I can help you understand and solve Archimedes' principle in this scenario. Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. In this case, the barge is floating in fresh water, so the buoyant force acting on it is equal to the weight of the water it displaces.

To solve this problem, we first need to find the volume of water displaced by the barge. Since the barge is rectangular with a length of 5 meters and a width of 2 meters, the volume can be calculated by multiplying these dimensions together: 5m x 2m = 10 cubic meters.

Next, we need to find the weight of this volume of water. The density of water is given as 1000 kg per cubic meter, so we can multiply the density by the volume to find the weight: 1000 kg/m^3 x 10 m^3 = 10,000 kg.

Now, we can use this weight to calculate the depth that the barge will sink when the 800 kg load is added. Since the buoyant force is equal to the weight of the water displaced, the barge will sink until the buoyant force is equal to the total weight of the barge and the load.

Let's represent the depth that the barge will sink as "h". We can set up the following equation:

Buoyant force = Weight of barge + Weight of load

or

ρgh = (m_barge + m_load)g

where ρ is the density of water, g is the acceleration due to gravity (9.8 m/s^2), m_barge is the mass of the barge, and m_load is the mass of the load.

We know that the barge has a mass of 10,000 kg (from the weight of the water displaced), and the load has a mass of 800 kg. Substituting these values into the equation, we get:

(1000 kg/m^3)(9.8 m/s^2)h = (10,000 kg + 800 kg)(9.8 m/s^2)

Solving for h, we get:

h = 0.098 meters

Therefore, the barge will sink 0.098 meters (or approximately 9.8 cm) when the