You decide to repeat Archimedes experiment and determine the density of a candle holder. you suspend it from a spring scale and scale reads 8.0N. You then lower the holder into a tub of water until completely submerged and it reads 5.0N. what is the volume and density of the candle holder? What does the scale read when the holder is 75% submerged in water.
8.0N-5.0N=3.0N
I know buoyant force=density*volume*gravity for fluid
8 - 5 = 3 N. M*g = 3, M = 3/9.8 = 0.306 kg = Mass of water displaced.
V*D = 306 grams.
V*1 = 306, V = 306 cm^3. volume of water displaced = volume of candle holder.
M*g = 8 N. M = 8/g = 8/9.8 = 0.816 kg = Mass of candle holder.
D = 816g/306cm^3 = 2.67 g/cm^3.
To determine the volume and density of the candle holder, we can use the principle of buoyancy. Here are the steps to follow:
1. Calculate the buoyant force when the candle holder is submerged in water by using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. The difference between the initial reading (8.0 N) and the submerged reading (5.0 N) on the scale gives us the weight of the water displaced by the candle holder: 8.0 N - 5.0 N = 3.0 N.
2. Determine the volume of water displaced using the formula for density: buoyant force = density * volume * gravity. Rearrange the formula to solve for volume: volume = buoyant force / (density * gravity).
3. Substitute the known values into the equation: volume = 3.0 N / (density of water * gravity).
4. The density of water can be assumed to be approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s². Substituting these values, we get: volume = 3.0 N / (1000 kg/m³ * 9.8 m/s²).
5. Calculate the volume to find the density of the candle holder.
To find the scale reading when the holder is 75% submerged in water, follow these steps:
1. Determine the portion of the volume of the candle holder that is submerged in water. Since the holder is completely submerged, the fraction of the holder underwater is equal to its volume relative to the volume of water displaced.
2. Calculate the new volume of water displaced by multiplying the previous volume by the fraction of the holder underwater.
3. Calculate the new buoyant force using the new volume of water displaced.
4. Finally, subtract the new buoyant force from the weight of the holder in air (8.0 N) to find the scale reading when the holder is 75% submerged.