To determine the density of sand using the provided instruments, the student can follow these steps:
Step 1: Measure the mass of the sand
The mass of the sand can be calculated using the mass of the density bottle with sand and the mass of the empty density bottle: \[ \text{Mass of sand} (M_s) = M_2 - M_1 \] Where:
- \(M_2 = 550 , \text{g}\) (mass of density bottle and sand)
- \(M_1 = 200 , \text{g}\) (mass of density bottle)
Calculating: \[ M_s = 550 , \text{g} - 200 , \text{g} = 350 , \text{g} \]
Step 2: Determine the volume of the sand
Next, we find the volume of water displaced by the sand when it is placed in the density bottle. The mass of the density bottle with water is given as:
- \(M_4 = 300 , \text{g}\) (mass of density bottle and water)
The volume of water (which will be the same volume as the sand, since they occupy the same space when the sand is added) can be calculated using the mass of the density bottle with water and the mass of the empty density bottle: \[ \text{Mass of water} (M_w) = M_4 - M_1 \] Calculating: \[ M_w = 300 , \text{g} - 200 , \text{g} = 100 , \text{g} \]
Now, convert the mass of water to volume. The density of water is approximately \(1 , \text{g/cm}^3\), thus: \[ \text{Volume of water} (V_w) = \text{Mass of water} = 100 , \text{cm}^3 \]
Step 3: Calculate the density of sand
The density of the sand can now be calculated using the formula for density: \[ \text{Density} (\rho) = \frac{\text{Mass}}{\text{Volume}} \] Substituting the values we have: \[ \rho_s = \frac{M_s}{V_w} = \frac{350 , \text{g}}{100 , \text{cm}^3} \]
Calculating: \[ \rho_s = 3.5 , \text{g/cm}^3 \]
Conclusion
The density of the sand is 3.5 g/cm³.