How Does Container Density Affect Its Sinking and Rising Velocity?

[kurtdtn]

Homework Statement

80 m² Surface Area; 1,519,875 Pascals Pressure; 640 m³ Volume:
2 m x 8 m x 40 m Dimensions; Mass 650,000 kg; and there is 250,000 liters of water inside.

If I let go of the container and allow it to sink what will be the velocity of sinking?
If I pump out 20,000 liters of water so that the container is now buoyant how fast will it rise to the surface?

Homework Equations

Weight = mg 650,000 kg * 9.8 m/s = 6374323 N
P =F/A 6374323 N / 80 m²
650,000 kg - 20,000 kg = 630,000 kg
640 m³ of water = 640,000 kg
Mass of Object - Apparent Mass when submerged = Density of Water x Volume

The Attempt at a Solution

650,000 kg - 640,000 kg = +10,000 kg = 10,000/640,000 = 1.6% * 9.8 m/s = .15 m/s upward or downward velocity depending on whether there is 250,000 liters inside or 230,000 liters inside

 

[KataKoniK]

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To calculate the velocity of sinking, we first need to find the buoyant force acting on the container. This can be found using the formula Fb = ρVg, where ρ is the density of water (1000 kg/m3), V is the volume of water displaced (640 m3), and g is the acceleration due to gravity (9.8 m/s2). Plugging in these values, we get Fb = (1000 kg/m3)(640 m3)(9.8 m/s2) = 6,272,000 N.

Next, we need to find the weight of the container, which is given by the formula W = mg, where m is the mass of the container (650,000 kg) and g is the acceleration due to gravity (9.8 m/s2). Plugging in these values, we get W = (650,000 kg)(9.8 m/s2) = 6,370,000 N.

Since the buoyant force is less than the weight of the container, it will sink. The velocity of sinking can be found using the formula v = √(2gh), where h is the depth the container sinks to. Since the container is sinking in water, we can assume that the acceleration due to gravity is equal to the buoyancy force divided by the mass of the container. Therefore, we can rewrite the formula as v = √(2Fb/m). Plugging in the values for Fb and m, we get v = √(2(6,272,000 N)/(650,000 kg)) = 2.26 m/s. This is the velocity at which the container will sink.

To calculate the velocity of rising after pumping out 20,000 liters of water, we need to first find the new volume of water displaced. Since 20,000 liters is equal to 20 m3, the new volume of water displaced will be 640 m3 - 20 m3 = 620 m3. Using the same formula as before, we can find the new buoyant force to be Fb = (1000 kg/m3)(620 m3)(9.8 m/s2) = 6,076,000 N.

Next, we need to find the new weight of the container, which is given by the formula W = mg, where m is the mass of the container (650,000 kg -

 

[Mene]

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The rate of sink and float is determined by the density of the object and the surrounding fluid. In this case, the container has a density of 650,000 kg/640 m3 = 1015.625 kg/m3. The density of water is 1000 kg/m3, so the container is slightly denser than water and will sink.

To calculate the velocity of sinking, we can use the formula v = √(2gh), where g is the acceleration due to gravity (9.8 m/s2) and h is the height the object has sunk. In this case, h = 40 m, so the velocity of sinking would be approximately 28.4 m/s.

If 20,000 liters of water is pumped out, the density of the container will decrease. The new density would be (650,000 kg - 20,000 kg)/640 m3 = 1010.9375 kg/m3. This is now less than the density of water, so the container will float.

To calculate the velocity of rising, we can use the same formula, but with h = 40 m - 2 m = 38 m (since the container has risen 2 m due to the decrease in mass). The velocity of rising would be approximately 27.6 m/s.

It is important to note that the actual velocity may be different due to factors such as drag and buoyancy forces, which were not taken into account in this calculation.