An object weighs 20N in air and 15N when fully immersed in water.calculate;volume of an object,(ii)density of an object
weight of water displaced = 5 N
mass of water displaced = F/a = 5 N / 9.81 m/s^2 = 0.510 kg
density of water = 1000 kg / m^3
so volume = 0.5510 kg *1 m^3 / 1000 kg = 5.51 * 10^-4 m^3
density = mass /volume = ( 20/9.81) / 5.51*10^-4 = 0.37 *10^4 kg/m^3
= 3.7 *10^3 kg/m^3
or 3.7 times the density of water
I saw that the weight was reduced by 1/4, so I was confused by that density of 3.7
somehow we went from 0.510 to 0.5510 kg
picking up where that happened,
so volume = 0.510 kg *1 m^3 / 1000 kg = 5.1 * 10^-4 m^3
density = mass /volume = ( 20/9.81) / 5.1*10^-4 = 0.3997 *10^4 kg/m^3
= 4.0 *10^3 kg/m^3
or 4.0 times the density of water
To calculate the volume of an object, we can make use of Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
(i) Calculating the volume of the object:
1. First, find the difference between the weight of the object in the air and the weight of the object when fully immersed in water.
Difference = Weight in air - Weight in water = 20N - 15N = 5N
2. Since the weight of the water displaced by the object is equal to the difference, we can equate it to the buoyant force acting on the object.
Buoyant force = Weight of water displaced = 5N
3. The buoyant force acting on an object submerged in a fluid is given by the formula:
Buoyant force = Density of fluid × Volume of fluid displaced × Acceleration due to gravity
4. In this case, the fluid is water, and the acceleration due to gravity can be taken as approximately 9.8 m/s^2.
Eq. 1: Buoyant force = Density of water × Volume of water displaced × 9.8 m/s^2
5. Rearrange Eq. 1 to calculate the volume of water displaced:
Volume of water displaced = Buoyant force / (Density of water × 9.8 m/s^2)
6. Substitute the given values to find the volume of water displaced by the object.
Once you have the volume of the water displaced, it will be the same as the volume of the object since both are fully submerged.
(ii) Calculating the density of the object:
1. The density of an object is defined as its mass per unit volume.
Density = Mass / Volume
2. Given the weight of the object in air, we can find the mass using the formula:
Weight = Mass × Acceleration due to gravity
Eq. 2: 20N = Mass × 9.8 m/s^2
3. Rearrange Eq. 2 to calculate the mass of the object:
Mass = Weight / 9.8 m/s^2
4. Now, substitute the calculated volume of the object along with the given mass into the density formula to find the density of the object.
By following these steps, you'll be able to calculate the volume and density of the object.