Calculate Depth of Floating Instrument: 0.219 kg in Water

In summary, the conversation discusses the calculation of the depth, z, of the bottom end of a hollow brass tube when it is floated in pure water. Through the use of various laws and formulas, it is determined that the depth can be found using the formula z = m/(πr2ρ). After some confusion with the variable "n", it is clarified that it should be "pi" in the formula.
  • #1
DDS
171
0
A hollow brass tube (diameter = 3.23 cm) is sealed at one end and loaded with lead shot to give a total mass of 0.219 kg. When the tube is floated in pure water, what is the depth, z, of its bottom end?

through manipulation of some laws i have broken it down to this stage:

z = m/(πr2ρ)

where:

m=0.219 kg
r=0.0323/2=0.01615m
p=1000 kg/m^3

thus i have :

z= 0.219/ n(0.01615)2(1000)

but what the hell is n... i know its not the incidencs for water because nothing is getting reflected and i just tried to plug it into see what would happen and it doesn't work any help?
 
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  • #2
That's not"n", it's "pi" (3.1415926535...)

It came from the formula for the area of a circle.
 
  • #3
thanx so mucn, silly mistake on my part
 

What is the formula for calculating depth of a floating instrument?

The formula for calculating depth of a floating instrument is: depth = (weight of the instrument in air - weight of the instrument in water) / density of water.

Why is it important to calculate the depth of a floating instrument?

Calculating the depth of a floating instrument is important because it allows us to determine the displacement of the instrument, which can be used to measure the volume of an object or the buoyancy of a material.

What is the weight of the floating instrument in water?

The weight of the floating instrument in water can be calculated by subtracting the weight of the instrument in air from its weight in water.

What is the density of water?

The density of water varies slightly depending on temperature and salinity, but on average it is 1000 kg/m3.

What other factors may affect the accuracy of the calculated depth?

The accuracy of the calculated depth may be affected by factors such as the temperature and salinity of the water, the shape and density of the floating instrument, and any external forces acting on the instrument (e.g. wind or waves).

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