What is the volume of the secret cavity in this submerged sculpture?

In summary, the small sculpture made of brass has a density of 8470 kg/m cubed and is believed to have a secret central cavity. When submerged in water, its weight decreases from 15.76N to 13.86N due to the buoyant force. To find the volume of the secret cavity, we can use Archimedes' principle and the relationship between density, mass, and volume. The volume of the fluid displaced is equal to the volume of the submerged object, which can help us solve for the volume of the cavity.
  • #1
skonstanty
11
0
A small sculpture made of brass (density = 8470 kg/m cubed) is believed to have a secret central cavity. The weight of the sculpture in air is 15.76N. When it is submerged in water, the weight is 13.86 N. What is the volume of the secret cavity?
 
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  • #2
what have you done?

you must be familiar with archimedes principle, i suppose.

Well you know the buoyant force is equal to the mass of the fluid displaced times gravity. When the object is submerged, its weight is less due to the buoyant force.

Use the relationship [itex] \rho = \frac{m}{v} [/itex] in the problem, and remember the volume of the fluid displaced is equal to the volume of what is submerged (in this case the entire object).
 
  • #3


To calculate the volume of the secret cavity, we can use the formula:
Volume = (Weight in air - Weight in water) / Density of brass

Substituting the given values, we get:
Volume = (15.76N - 13.86N) / 8470 kg/m^3
= 1.9N / 8470 kg/m^3
= 0.000224 m^3

Therefore, the volume of the secret cavity in this submerged sculpture is 0.000224 cubic meters.
 

1. What is volume in water problem?

Volume in water problem is a scientific concept that refers to the measurement of the amount of space occupied by a substance in water. It is often used in physics and chemistry to calculate the displacement of an object in water or to determine the concentration of a solute in a solution.

2. How is volume in water problem calculated?

The volume of an object in water can be calculated by measuring the amount of water displaced when the object is submerged in a container of water. This is known as the Archimedes' principle. The volume of a solute in a solution can be calculated by dividing the mass of the solute by its density in water.

3. What units are used to measure volume in water problem?

The most common units used to measure volume in water problem are liters (L) and milliliters (mL). In some cases, cubic meters (m3) or cubic centimeters (cm3) may also be used. It is important to use the correct units and convert between them if necessary to ensure accurate calculations.

4. How does temperature affect volume in water problem?

Temperature can affect volume in water problem because water expands as it heats up and contracts as it cools down. This can lead to changes in the volume of an object submerged in water or the volume of a solute dissolved in water. It is important to take into account the temperature when performing volume calculations in water.

5. What are some real-life applications of volume in water problem?

Volume in water problem has many practical applications, such as determining the buoyancy of ships, measuring the concentration of chemicals in water for environmental testing, and calculating the amount of medication to be given to a patient based on their body weight. It is also used in industries such as oil and gas, where the volume of a liquid must be accurately measured for transportation and storage purposes.

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