An object weighs 0.25N in air and
0.01N when immersed in water.
Calculate
(a) its relative density
(b) its apparent weight in a liquid of density 800kgm^-3
density water = 1000 kg/m^3
g = 9.81 m/s^2
Volume = V
mass = rho V
weight = rho (9.81) V = 9.81 rho V
Buoyancy = .25 - .01 = .24 N
so
.24 = 1000 (9.81)V
V = .0245 *10^-3 m^3
m = .25 N/9.81 = .0255 Kg
rho = m/V = 1.04 * 10^3
= 1040 Kg/m^3 answer (a)
new buoyancy = 800*.0245*10^-3 *9.81 = .193 N
apparent weight = .25 -.193 Newtons
=
it's great thank you Damon
Well, I have to say, this object must be really popular at parties, always looking so light in water! Let's find out its relative density and apparent weight in a liquid of density 800 kg/m³.
(a) To find the object's relative density, we can use the formula:
Relative Density = (Weight in Air) / (Weight in Air - Weight in Water)
Plugging in the given values, we get:
Relative Density = 0.25N / (0.25N - 0.01N)
= 0.25N / 0.24N
= 1.04
So, the object's relative density is approximately 1.04.
(b) Now, to calculate its apparent weight in a liquid with a density of 800 kg/m³, we can use the formula:
Apparent Weight = Weight in Air - (Density of Liquid) * (Volume of Object) * (g)
Since the volume of the object is not provided, we can't calculate its apparent weight. But hey, at least we discovered its relative density, right?
To calculate the relative density and the apparent weight, we can use the concept of buoyancy.
(a) Relative Density:
The relative density (also known as specific gravity) of an object is the ratio of its density to the density of a reference substance, usually water. In this case, we can calculate the relative density using the weights in air and water.
The weight in air is 0.25 N, and the weight in water is 0.01 N. The difference in weight between the two states is due to the buoyancy force acting on the object.
The buoyancy force is equal to the weight of the water displaced by the object, and it acts in an upward direction. Therefore, the buoyancy force can be calculated as the weight in air minus the weight in water:
Buoyancy force = Weight in air - Weight in water
= 0.25 N - 0.01 N
= 0.24 N
Now, we can use Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. The buoyancy force is also equal to the weight of the water displaced by the object.
The relative density can be calculated as the ratio of the weight of the object to the weight of the displaced water:
Relative density = Weight in air / (Weight in air - Buoyancy force)
= 0.25 N / (0.25 N - 0.24 N)
= 0.25 N / 0.01 N
= 25
Therefore, the relative density of the object is 25.
(b) Apparent Weight in a Liquid:
To calculate the apparent weight of the object in a liquid, we need to consider the buoyant force due to the liquid. The buoyant force is equal to the weight of the liquid displaced by the object.
The apparent weight can be calculated as the weight in air minus the buoyancy force:
Apparent weight = Weight in air - Buoyancy force
We are given that the density of the liquid is 800 kg/m^3. Therefore, the buoyancy force can be calculated as the weight of the liquid displaced by the object:
Buoyancy force = Density of liquid * Volume of object * Acceleration due to gravity
To find the volume of the object, we can use the formula:
Volume of object = (Weight in air - Weight in liquid) / Density of liquid
= (0.25 N - 0.01 N) / (800 kg/m^3 * 9.8 m/s^2)
= 0.24 N / (800 kg/m^3 * 9.8 m/s^2)
≈ 3.06 x 10^(-5) m^3
Now, we can calculate the buoyancy force:
Buoyancy force = 800 kg/m^3 * (3.06 x 10^(-5) m^3) * 9.8 m/s^2
≈ 0.00237 N
Finally, we can calculate the apparent weight in the liquid:
Apparent weight = Weight in air - Buoyancy force
= 0.25 N - 0.00237 N
≈ 0.2476 N
Therefore, the apparent weight of the object in a liquid with a density of 800 kg/m^3 is approximately 0.2476 N.
To calculate the relative density of an object, we can use the formula:
Relative Density = (Weight in Air) / (Weight in Air - Weight in Water)
(a) Weight in Air = 0.25N
Weight in Water = 0.01N
Relative Density = (0.25N) / (0.25N - 0.01N)
= (0.25N) / (0.24N)
= 1.04
Therefore, the relative density of the object is 1.04.
To calculate the apparent weight of the object in a liquid of density 800 kg/m³, we can use the formula:
Apparent Weight = Weight in Air - (Density of Liquid) * (Volume of Object) * (Acceleration due to Gravity)
(b) Weight in Air = 0.25N
Density of Liquid = 800 kg/m³
Volume of Object = ?
To find the volume of the object, we need to know its mass and density. Since we only have the weight in air and water, we cannot directly calculate the volume. However, we can make an assumption that the density of the object is the same as the density of the liquid, which is 800 kg/m³.
Density of Object = 800 kg/m³
Now, we can calculate the volume using the formula:
Volume = Mass / Density
Since the weight is given, we need to convert it to mass using the formula:
Weight = Mass * Acceleration due to Gravity
Rearranging the formula, we get:
Mass = Weight / Acceleration due to Gravity
Acceleration due to Gravity = 9.8 m/s²
Mass = 0.25N / 9.8 m/s²
Once we have the mass, we can calculate the volume:
Volume = Mass / Density
= (0.25N / 9.8 m/s²) / 800 kg/m³
Now that we have the volume, we can calculate the apparent weight:
Apparent Weight = Weight in Air - (Density of Liquid) * (Volume of Object) * (Acceleration due to Gravity)
= 0.25N - (800 kg/m³) * [(0.25N / 9.8 m/s²) / 800 kg/m³] * 9.8 m/s²
Calculating this expression will give us the apparent weight of the object in a liquid of density 800 kg/m³.