A hollow brass cylinder is weighed on a pan balance (kitchen scale) which read in kg. The scale reading is 5.56 kg. The brass cylinder is now removed from the scale and is replaced by a beaker of liquid density 1.56 * 10^3 kg/m^3; the scale now reads 17.50 kg. The brass cylinder is then suspended from a thread, and it is lowered into the liquid until it is completely immersed but does not touch the bottom of the beaker. The reading of the balance increases from 17.50 kg to 28.28 kg when the cylinder is immersed in the liquid. The density of brass is 8.47 * 10^3 kg/m^3.
(I) Calculate the volume of metal in the cylinder.
(II) Calculate the upthrust (buoyancy force) exerted on the hollow cylinder when it is totally immersed in the liquid.
(III) Calculate the volume of the hollow space inside the cylinder.
something is confusing me. How can the mass of the liquid+brass combined be greater than each separately?
Not sure but that's how the question goes.
alexandria, something is wrong with the construction of the problem. The weight of two people on a scale cannot be greater than the sum of both their weights.
It's ok thank you anyway
I think it would be; density difference: 8.47 * 10^3 kg/m^3 - 1.56 * 10^3 kg/m^3 = 6.91kg/m^3
Change in weight we have 28.28-17.50= 10.78kg
mass/density=volume
10.78/6.91=1.56
(I) To calculate the volume of metal in the cylinder, we need to use the relationship between mass, density, and volume.
First, let's find the mass of the brass cylinder. The scale initially reads 5.56 kg when the brass cylinder is placed on it.
Next, let's find the volume of the brass cylinder by dividing the mass by the density:
Volume = Mass / Density = 5.56 kg / (8.47 * 10^3 kg/m^3)
(II) To calculate the upthrust (buoyancy force) exerted on the hollow cylinder when it is immersed in the liquid, we need to use Archimedes' principle. Archimedes' principle states that the buoyant force experienced by an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
The change in scale reading when the brass cylinder is immersed in the liquid is given as 28.28 kg - 17.50 kg = 10.78 kg.
Therefore, the buoyant force on the brass cylinder is equal to the weight of the liquid it displaces, which is equal to the change in scale reading: Buoyant force = 10.78 kg * 9.8 m/s^2 (acceleration due to gravity)
(III) To calculate the volume of the hollow space inside the cylinder, we subtract the volume of the metal from the total volume of the cylinder.
The total volume of the cylinder is the volume of the liquid displaced when the cylinder is immersed. We can calculate that using the change in scale reading:
Total Volume = Change in Scale Reading / Density of Liquid = 10.78 kg / (1.56 * 10^3 kg/m^3)
Finally, subtract the volume of the metal from the total volume to find the volume of the hollow space inside the cylinder.