To find the specific gravity of the wax, we will follow these steps:
### Step 1: Determine the weight of the wax in air
The weight of the wax in air is given as:
\[ W_{\text{wax}} = 18.03 \, \text{g} \]
### Step 2: Determine the weight of the metal in water
The weight of the metal in water is given as:
\[ W_{\text{metal, water}} = 17.03 \, \text{g} \]
### Step 3: Determine the combined weight of the wax and metal in water
When the wax and the metal are tied together, their combined weight in water is:
\[ W_{\text{combined, water}} = 15.23 \, \text{g} \]
### Step 4: Calculate the buoyant force acting on the wax and metal
The apparent weight in water is given by the equation:
\[ W_{\text{metal}} - F_{\text{b, metal}} + W_{\text{wax}} - F_{\text{b, wax}} = W_{\text{combined, water}} \]
Where:
- \( F_{\text{b, metal}} \) is the buoyant force on the metal.
- \( F_{\text{b, wax}} \) is the buoyant force on the wax.
From the information given, we can express this as:
\[ W_{\text{metal}} + W_{\text{wax}} - (F_{\text{b, metal}} + F_{\text{b, wax}}) = W_{\text{combined, water}} \]
Substituting the known values:
\[ 17.03 + 18.03 - (F_{\text{b, metal}} + F_{\text{b, wax}}) = 15.23 \]
### Step 5: Solve for the total buoyant force
Calculating the left side:
\[ 35.06 - (F_{\text{b, metal}} + F_{\text{b, wax}}) = 15.23 \]
Rearranging gives:
\[ F_{\text{b, metal}} + F_{\text{b, wax}} = 35.06 - 15.23 = 19.83 \, \text{g} \]
### Step 6: Relate the buoyant force to the volume of the wax
The buoyant force is also given by the formula:
\[ F_{\text{b}} = \rho_{\text{fluid}} \cdot V \cdot g \]
Where:
- \( \rho_{\text{fluid}} \) is the density of the fluid (water in this case).
- \( V \) is the volume of the object submerged.
- \( g \) is the acceleration due to gravity.
Assuming the density of water is approximately \( 1 \, \text{g/cm}^3 \), we can express the buoyant force on the wax as:
\[ F_{\text{b, wax}} = \rho_{\text{water}} \cdot V_{\text{wax}} \cdot g = V_{\text{wax}} \cdot g \]
### Step 7: Set up the equation for the density of wax
From the weight of the wax:
\[ W_{\text{wax}} = \rho_{\text{wax}} \cdot V_{\text{wax}} \cdot g \]
Substituting the values we have:
\[ 18.03 = \rho_{\text{wax}} \cdot V_{\text{wax}} \cdot g \]
### Step 8: Combine the equations to find the specific gravity
We have:
\[ \rho_{\text{wax}} \cdot V_{\text{wax}} \cdot g = 18.03 \]
And:
\[ V_{\text{wax}} \cdot g = 19.83 \]
Dividing these two equations:
\[ \frac{\rho_{\text{wax}} \cdot V_{\text{wax}} \cdot g}{V_{\text{wax}} \cdot g} = \frac{18.03}{19.83} \]
This simplifies to:
\[ \rho_{\text{wax}} = \frac{18.03}{19.83} \]
### Step 9: Calculate the specific gravity
The specific gravity of the wax is defined as:
\[ \text{Specific Gravity} = \frac{\rho_{\text{wax}}}{\rho_{\text{water}}} \]
Since \( \rho_{\text{water}} \approx 1 \, \text{g/cm}^3 \):
\[ \text{Specific Gravity} = \frac{18.03}{19.83} \]
### Final Calculation
Calculating the specific gravity:
\[ \text{Specific Gravity} \approx 0.909 \]
### Conclusion
The specific gravity of the wax is approximately \( 0.909 \).
---
