An object weighed 7N in air and 5N in water.If the object is immersed completely in water and the density of water is 1000kg m-3, calculate the ;
(a) weight of water displaced,
(b) Volume of the object
(c) density of the object
(a) 7 N - 5 N =
(b) the object displaced 2 N of water
... w = m g ... 2 = m * 9.8
... the volume (in L) is equal to the mass of water (in kg)
(c) the 7 N object has the same volume as 2 N of water
... its density is 7/2 water's density
To find the answers to these questions, we can use some principles of buoyancy and density.
(a) Weight of water displaced:
According to Archimedes' principle, when an object is immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced. The weight of the water displaced is equal to the difference between the weight of the object in air and in water.
Weight of water displaced = Weight in air - Weight in water
Weight of water displaced = 7N - 5N
Weight of water displaced = 2N
Therefore, the weight of water displaced is 2N.
(b) Volume of the object:
The volume of water displaced by the object is equal to the volume of the object itself. We can use the formula:
Density = Mass / Volume
Here, we know the density of water (1000 kg/m^3) and the weight of water displaced (2N). Since we don't know the mass directly, we can convert the weight to mass using the formula:
Weight = Mass x Gravity
2N = Mass x 9.8 m/s^2
Solving for mass, we get:
Mass = 2N / 9.8 m/s^2
Now, we can use the density formula to find the volume:
Density = Mass / Volume
Rearranging the formula:
Volume = Mass / Density
Substituting the known values:
Volume = (2N / 9.8 m/s^2) / 1000 kg/m^3
Simplifying, we get:
Volume = 0.000204 m^3
Therefore, the volume of the object is 0.000204 m^3.
(c) Density of the object:
The density of an object can be calculated by dividing its mass by its volume.
Density = Mass / Volume
To find the mass, we can use the weight of the object in air, using the formula:
Weight = Mass x Gravity
7N = Mass x 9.8 m/s^2
Solving for mass, we get:
Mass = 7N / 9.8 m/s^2
Now, we can calculate the density:
Density = Mass / Volume
Substituting the known values:
Density = (7N / 9.8 m/s^2) / 0.000204 m^3
Simplifying, we get:
Density = 34215.6863 kg/m^3
Therefore, the density of the object is 34215.6863 kg/m^3.