a metal object is suspended from a spring balance scale. the scale reads 800 N when it is suspended in air and 700 N when the object is completely submerged in water. find the buoyant force, the volume and the density of the metal.
bouyant force=100N
this force of 100N is equal to the weight of volume of the water displaced.
100N=densitywater*g*volumewater
solve for the volume of water displaced, that is equal to the volume of the metal submerged.
Now, that volume is submerged, so
density=mass/volume= (700/g)/Volume
To find the buoyant force, volume, and density of the metal, we can use the principles of buoyancy and Archimedes' principle.
Step 1: Calculate the weight of the object in air:
The scale reads 800 N when the object is suspended in air. This is the weight of the object since it's not experiencing any buoyant force.
Weight of the object in air = 800 N
Step 2: Calculate the weight of the object in water:
The scale reads 700 N when the object is completely submerged in water. This reading includes the weight of the object minus the buoyant force acting on it.
Weight of the object in water = 700 N
Step 3: Calculate the buoyant force:
The buoyant force is the difference between the weight of the object in air and the weight of the object in water.
Buoyant force = Weight of the object in air - Weight of the object in water
Buoyant force = 800 N - 700 N
Buoyant force = 100 N
Step 4: Calculate the volume of the object:
According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid displaced by the object. In this case, the fluid is water.
Buoyant force = Weight of the fluid displaced
100 N = density of water * volume of the object * gravity
Since we want to calculate the volume of the object, we rearrange the equation:
Volume of the object = Buoyant force / (density of water * gravity)
Assuming the density of water is 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2:
Volume of the object = 100 N / (1000 kg/m^3 * 9.8 m/s^2)
Volume of the object ≈ 0.01 m^3
Step 5: Calculate the density of the metal:
The density of an object can be calculated by dividing its mass by its volume:
Density of the metal = Mass of the metal / Volume of the object
We haven't been given the mass of the metal directly, but we can use the weight of the object in air to calculate it:
Mass of the metal = Weight of the object in air / Acceleration due to gravity
Assuming the acceleration due to gravity is 9.8 m/s^2:
Mass of the metal = 800 N / 9.8 m/s^2
Mass of the metal ≈ 81.6 kg
Density of the metal = Mass of the metal / Volume of the object
Density of the metal = 81.6 kg / 0.01 m^3
Density of the metal ≈ 8160 kg/m^3
So, the buoyant force is 100 N, the volume of the metal object is approximately 0.01 m^3, and the density of the metal is around 8160 kg/m^3.
To find the buoyant force, we can use Archimedes' Principle, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Step 1: Find the weight of the object in air.
The scale reads 800 N when the object is suspended in air.
Step 2: Find the weight of the object in water.
The scale reads 700 N when the object is completely submerged in water.
Step 3: Calculate the buoyant force.
The difference between the weight of the object in air and in water is equal to the buoyant force:
Buoyant force = Weight in air - Weight in water
Buoyant force = 800 N - 700 N
Buoyant force = 100 N
So, the buoyant force acting on the object is 100 N.
To find the volume and density of the metal, we need to use the relationship between buoyant force and the weight of the fluid displaced by the object.
Step 4: Calculate the weight of the water displaced.
The weight of the water displaced is equal to the buoyant force since the object is submerged in water:
Weight of water displaced = Buoyant force = 100 N
Step 5: Calculate the volume of the metal.
The volume of the metal can be found using the density of water:
Volume = Weight of water displaced / Density of water
The density of water is approximately 1000 kg/m^3.
Before we proceed, we need to convert the weight of water displaced from Newtons to kilograms by dividing it by the acceleration due to gravity (g ≈ 9.8 m/s^2):
Weight of water displaced (in kg) = Weight of water displaced (in N) / g
Step 6: Plug in the known values to find the volume.
Volume = (Weight of water displaced (in kg) / Density of water) in cubic meters
Step 7: Calculate the density of the metal.
Density = Mass / Volume
Since we know the weight of the object in air and the volume, we can calculate the mass using the formula:
Mass = Weight in air (in kg) / g
Finally, we can calculate the density of the metal by dividing the mass by the volume.
By following these steps, you can determine the buoyant force, volume, and density of the metal object.