Calculating Volume of Sample in Air and Water

[badman]

im having a really hard time trying to figure this out.
An ore sample weighs 19.8 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.5 N.

Find the total volume of the sample.
Take the density of water to be rho_water = 1000 kg/m^3 and the free fall acceleration to be g = 9.80 m/s^2.


heres the equation i figured out for this type of problem.

force of buoyancy=density*volume* gravity.

alright is the force of buoyancy for air and water 19.8 and 11.5 respectively?
if so won't i just have to multiply grvity times thhier densities divided by the force to find the volumes then add them up?

 

[Fermat]

You can neglect the buoyancy for air - it's neglible.
The difference in tension in the cord is 19.8 - 11.5 = 8.3 N.
The displacement of the water by the mass has provided this buoyancy force (8.3N)

now use the eqn you worked out.

 

[thepatientmental]

Calculating the volume of a sample in both air and water can be confusing, but with the right equation and understanding, it can be easily solved. Let's break down the problem step by step.

First, we need to understand the concept of buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyancy, which is equal to the weight of the fluid it displaces. This means that the force of buoyancy is dependent on the density of the fluid, the volume of the object, and the gravity acting on it.

In this problem, we are given the weight of the sample in air (19.8 N) and the tension in the cord when the sample is immersed in water (11.5 N). We can use this information to find the volume of the sample.

Let's start with the sample in air. We can use the equation you mentioned, force of buoyancy = density * volume * gravity. We know the force of buoyancy (19.8 N) and the density of air (which is approximately 1.2 kg/m^3). We also know the value of gravity (9.80 m/s^2). So, we can rearrange the equation to solve for volume:

volume = force of buoyancy / (density * gravity)
volume = 19.8 N / (1.2 kg/m^3 * 9.80 m/s^2)
volume = 1.7 m^3

Next, let's look at the sample in water. We can use the same equation, but this time we need to use the density of water (1000 kg/m^3) and the force of buoyancy in water (11.5 N):

volume = 11.5 N / (1000 kg/m^3 * 9.80 m/s^2)
volume = 0.0012 m^3

Now, we need to find the total volume of the sample. To do this, we simply add the volumes calculated in air and water together:

total volume = 1.7 m^3 + 0.0012 m^3
total volume = 1.7012 m^3

So, the total volume of the sample is approximately 1.7012 m^3. I hope this helps you understand the process of calculating volume in air and water. Remember to always pay attention to the units and use the correct values for