A person got a metal rock, he knows this rock density is ρm, but he is worried that there might be a hole within the rock, how he found there is a hole or not? And how he found the fraction of the hole size to total rock size? write your experimental steps.
If ñm is the density of the rock with no holes, it can be compared to the actual density of the sample. Measure the volume of the rock, V and its mass, M.
V*ñm - M = missing mass due to hole(s)
= m
m/ñm = v = volume of hole(s)
v/V = fraction of sample that is holes
= (1/V)[m/ñm]
= (1/V)(V*ñm - M)/ñm
= 1 - [M/(V*ñm)]
how do fish use density in their lives?
To determine if the metal rock has a hole within it and estimate the fraction of the hole size to the total rock size, the following experimental steps can be followed:
1. Measure the mass of the metal rock using a scale and record it as m₁.
2. Fill a container with a known volume of water, V₀.
3. Carefully lower the metal rock into the water, ensuring that it is fully submerged.
4. Measure the increase in water volume in the container and record it as ΔV.
5. Calculate the density of water, ρw, at the experimental temperature using established tables or formulas.
6. Calculate the volume of the metal rock using the formula V = (m₁ / ρm).
7. Calculate the density of the metal rock using the formula ρ = (m₁ / V).
8. If the density of the metal rock is equal to or close to the known density of the particular metal, it suggests that there is no hole present within the rock. If the densities do not match, there might be a void or hole.
9. To estimate the fraction of the hole size to the total rock size, calculate the volume of the metal rock without the hole using the formula V₁ = (m₁ / ρm).
10. Subtract the calculated volume of the metal rock without the hole (V₁) from the measured volume of the metal rock (V) to get the volume of the hole (Vh).
11. Calculate the fraction of the hole size to the total rock size using the formula fraction = (Vh / V).
12. The obtained fraction will represent the relative size of the hole within the metal rock.
It's important to note that these experimental steps assume idealized conditions and may require additional calibration or corrections for accurate results.