Determining the Density of a Wooden Block using Archimedes’ Principle In this experiment, we will determine the density (p) of a wooden block by measuring the height (h) of the block above the water when it floats. We will use the equation to calculate the correct ratio equivalent to Vsubmerged / Vobject. (HINT: You shouldn’t have to calculate any volume) H (mm) h (mm) correct ratio Pobject Pobject object kglm? glcm? Wooden block A 31 Wooden block B 19 Wooden block C 29 16
The Correct Answer and Explanation is:
To determine the density of a wooden block using Archimedes’ principle, we can focus on the relationship between the height of the block submerged in water and the height above the water when the block floats. Archimedes’ principle states that the buoyant force acting on a submerged object is equal to the weight of the displaced fluid, which in this case is water.
Step 1: Understanding the Equation
When a wooden block floats on water, the block displaces a volume of water equal to the submerged portion of the block. The ratio of the submerged volume to the total volume of the block (Vsubmerged/Vobject) is directly related to the fraction of the block’s height that is submerged in water.
This ratio can be expressed as:VsubmergedVobject=hH\frac{V_{\text{submerged}}}{V_{\text{object}}} = \frac{h}{H}VobjectVsubmerged=Hh
Where:
- hhh is the submerged height of the block in water.
- HHH is the total height of the block above the water.
Step 2: Applying the Formula to Calculate Density
The density of an object can be determined from the relationship between the mass of the object and the volume of water it displaces. Since the wooden block is floating, the ratio of the submerged volume to the total volume gives us a measure of how much of the block is submerged in water. The fraction of the block submerged corresponds to the ratio of the block’s density to the density of water.
Thus, the density of the block (ρblock\rho_{\text{block}}ρblock) is given by:ρblock=ρwater×(VsubmergedVobject)\rho_{\text{block}} = \rho_{\text{water}} \times \left(\frac{V_{\text{submerged}}}{V_{\text{object}}}\right)ρblock=ρwater×(VobjectVsubmerged)
Where:
- ρwater\rho_{\text{water}}ρwater is the density of water (typically 1 g/cm³ at 4°C).
- VsubmergedVobject\frac{V_{\text{submerged}}}{V_{\text{object}}}VobjectVsubmerged is the ratio based on the height measurement.
Step 3: Determining the Correct Ratio
From the given data:
- Wooden block A has a total height (H) of 31 mm, and the submerged height (h) is not provided but can be inferred.
- Wooden block B has a total height of 19 mm, and similarly, the submerged height needs to be derived.
- Wooden block C has a total height of 29 mm, and the submerged height will be measured as well.
For each block, the ratio of the submerged height to the total height gives us the proportion of the block that is submerged. This ratio will be the key to calculating the density of each block.
Step 4: Using the Ratio for Density Calculation
If you know the submerged height for each block, you can substitute the values into the density formula for each block:
- For Wooden block A, calculate the ratio hA31\frac{h_A}{31}31hA.
- For Wooden block B, calculate the ratio hB19\frac{h_B}{19}19hB.
- For Wooden block C, calculate the ratio hC29\frac{h_C}{29}29hC.
Once you have the correct ratios, you can estimate the density of each wooden block relative to the density of water.
Conclusion
The floating behavior of the wooden blocks gives insight into their density. By measuring the submerged height and applying Archimedes’ principle, you can determine the ratio that corresponds to each block’s density in comparison to water. This method simplifies the calculation without requiring direct volume measurements of the blocks themselves.
