How do i compute for the volume if the density of ore is not given?

[raisatantuico]

Homework Statement

An ore sample weights 17.50 N in air. When th sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.20 N. What is the total volume of the object?

Homework Equations

B = rho * volume displaced* g

B= weight in air - weight apparent

The Attempt at a Solution

I took the tension in the string as equal to the apparent weight. So using that I computed for the buoyancy: 17.50N - 11.20N = 6.3N

So, 6.3N = rho*volume of water displaced *g

how do i compute for the volume if the density of ore is not given?

 

[JaredJames]

Volume of water displaced = volume of ore

You know the density of water so how about calculating the volume of water displaced?

Jared

 

[raisatantuico]

So, is it just 6.3N/(9.8*1000kg/m^3) = 6.43x10^-4 m^3

 

[JaredJames]

F_buoyant = density * volume * gravity

Rearranging gives F_buoyant / (density * gravity) = volume

6.3 / (9.8 * 1000) = 6.43x10^-4 m^3

Jared

 

[rwisz]

Without knowing the density of the ore, it is not possible to directly compute the volume of the object. However, there are a few steps you can take to potentially determine the volume of the object.

1. Use the buoyancy equation you have already set up: 6.3N = rho*volume of water displaced *g. Since the density of water is known, you can solve for the volume of water displaced.

2. Determine the density of the object by measuring its mass and volume. If you have access to a balance and a graduated cylinder, you can measure the mass of the object and the volume of water it displaces in the cylinder. Then, using the equation density = mass/volume, you can calculate the density of the object.

3. Use a reference table or database to find the average density of similar ores. If you know the type of ore you are working with, you can look up the average density of that type of ore and use that value to calculate the volume.

4. If none of the above options are possible, you can estimate the volume of the object based on its size and shape. This may not be as accurate as the other methods, but it can give you a rough estimate of the volume.

Overall, the key is to use the information you do have (such as the mass, buoyancy, and/or density) to solve for the volume of the object.