in air an object weighs 15n, when immersed in water it weighs 12n, when immersed in another liquid it weighs 13n. determine the density of the object and that of the other liquid
Its volume displaced 3 Newtons of water
3 Newtons = mass of water * g
g is about 9.81m/s^2
so mass of water =3/9.81 =0.306 kg
Water density is about 1000 kg/meter^3
0.306 kg * 10^-3m^3/kg = 3.06 *10^-4 m^3 volume
so
15 kg/3.06*10^-4 m^3 = 4.9*10^4 kg/m^3
if you want grams/cm^3
4.9*10^4 * 10^-6 m^3/cm^3 * 10^3 g/kg =49 g/cm^3
To determine the density of the object and the other liquid, we need to use the principle of buoyancy and the equation relating the weight of the object to the density of the liquid it's immersed in.
The principle of buoyancy 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. In other words, when an object is immersed in a liquid, it experiences an upward force (buoyant force) that opposes the force of gravity, reducing its weight.
Let's start by calculating the density of the object:
1. In air, the object weighs 15 N. This is its actual weight, considering the force of gravity acting on it. Therefore, its mass can be determined using the formula:
Weight = mass × gravity
15 N = mass × 9.8 m/s^2
Rearranging the equation to solve for mass:
mass = 15 N / 9.8 m/s^2 ≈ 1.53 kg
2. In water, the object weighs 12 N. However, the weight of the object in water is reduced due to the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the object. Therefore, we need to determine the weight of the water that is displaced by the object.
The weight of the displaced water is equal to the difference between the weight of the object in air and its weight in water:
Weight of displaced water = 15 N - 12 N = 3 N
Since the displaced water has the same mass as the object, we can use this weight to find its volume (assuming water density is 1000 kg/m^3):
Weight of displaced water = density of water × volume of water × gravity
3 N = 1000 kg/m^3 × volume of water × 9.8 m/s^2
Rearranging the equation to solve for volume:
volume of water = 3 N / (1000 kg/m^3 × 9.8 m/s^2) ≈ 0.00031 m^3
Since the volume of the water displaced is the same as the volume of the object:
volume of object = 0.00031 m^3
The density of the object can be calculated using the formula:
density = mass / volume
density of object = 1.53 kg / 0.00031 m^3 ≈ 4935.48 kg/m^3
Now, let's calculate the density of the other liquid:
3. In the other liquid, the object weighs 13 N. Similar to the previous step, we need to find the weight of the liquid displaced by the object:
Weight of displaced liquid = 15 N - 13 N = 2 N
Using the same reasoning as before, we can find the volume of the displaced liquid (assuming its density is D kg/m^3):
Weight of displaced liquid = density of liquid × volume of liquid × gravity
2 N = D kg/m^3 × volume of liquid × 9.8 m/s^2
Rearranging the equation to solve for volume:
volume of liquid = 2 N / (D kg/m^3 × 9.8 m/s^2)
The volume of the liquid displaced is equal to the volume of the object:
volume of object = volume of liquid
Therefore:
volume of liquid = 0.00031 m^3
The density of the other liquid can be calculated using the formula:
density = mass / volume
density of liquid = 1.53 kg / 0.00031 m^3 ≈ 4935.48 kg/m^3
Hence, the density of the object and the other liquid is approximately 4935.48 kg/m^3.