A 1.7 cm thick bar of soap is floating in water, with 1.1 cm of the bar underwater. Bath oil with a density of 890.0 kg/m3 is added and floats on top of the water. How high on the side of the bar will the oil reach when the soap is floating in only the oil.
To find out the height on the side of the soap bar where the oil will reach when the soap is floating in only the oil, we need to consider the principle of buoyancy and compare the densities of the soap, water, and oil.
First, let's analyze the situation with the soap bar floating in only water:
1. The soap bar is floating, which means its weight is equal to the buoyant force acting on it.
2. The buoyant force is equal to the weight of the water displaced by the submerged part of the soap bar.
3. Since the soap bar is floating, the buoyant force is also supporting the part of the bar above the water's surface.
4. The density of water is approximately 1000 kg/m3.
Given:
- Thickness of the soap bar: 1.7 cm
- Submerged height of the soap bar: 1.1 cm
Using these measurements, we can determine the submerged volume of the soap bar:
Submerged volume = Thickness × Submerged height
Submerged volume = 1.7 cm × 1.1 cm
Next, let's consider the situation when the soap bar is floating in only bath oil:
Given:
- Density of bath oil: 890.0 kg/m3
To find the height on the side of the soap bar where the oil will reach, we need to determine the submerged volume of the soap bar in the oil. For this, we need to calculate the volume of the oil displaced by the soap bar.
Submerged volume in oil = Volume of oil displaced
To find the volume of oil displaced, we need to compare the densities of the soap bar and the bath oil.
- If the density of the soap bar is greater than the density of bath oil, it will sink, and there will be no oil displaced.
- If the density of the soap bar is less than the density of bath oil, it will float, displacing an equal volume of oil.
Comparing the densities, we can see that the density of bath oil (890.0 kg/m3) is less than the density of water (1000 kg/m3). Hence, the soap bar will float in the bath oil.
Therefore, the submerged volume of the soap bar in the oil will be equal to the submerged volume of the soap bar in water.
Now, substitute the values into the equation:
Submerged volume in oil = Thickness × Submerged height
Submerged volume in oil = 1.7 cm × 1.1 cm
The calculated value for the submerged volume in oil gives you the volume of oil displaced by the soap bar. To determine the height on the side of the bar where the oil will reach, divide this volume by the thickness of the soap bar:
Oil height on bar = Submerged volume in oil / Thickness of soap bar
By substituting the values into the equation, you'll get the answer to the question.