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 determine the height on the side of the soap bar where the oil will reach, we need to consider the equilibrium conditions between the forces acting on the soap bar.
First, let's calculate the density of the soap bar. Given that the soap bar is floating, its average density must be equal to the density of the water. The density of water at room temperature is typically around 1000 kg/m3.
Next, we need to determine the height of the soap bar protruding above the water. Since 1.1 cm of the bar is submerged underwater, and the total thickness is 1.7 cm, the height above water would be 1.7 cm - 1.1 cm = 0.6 cm.
Now, let's introduce the bath oil with a density of 890.0 kg/m3. Since the oil is less dense than water, it will float on top of the water. We want to find the height at which the oil will reach on the side of the soap bar.
To determine the height, we use the concept of buoyancy. The buoyant force acting on the soap bar is equal to the weight of the displaced fluid. In this case, the displaced fluid is a combination of water and oil.
To find the height at which the oil reaches, we first need to calculate the volume of the soap bar submerged in the oil. We know the density of the oil (890.0 kg/m3) and the height of the soap bar protruding above the water (0.6 cm). Multiplying the two values together will give us the volume of the submerged portion in the oil.
Next, we convert the volume to cubic meters by dividing by 1000000 (since there are 1,000,000 cubic centimeters in a cubic meter).
Finally, we divide the volume by the width of the soap bar to get the height that the oil will reach on the side of the soap bar.
Please provide the width of the soap bar, and I can help you calculate the height at which the oil will reach.