An object has a weight of 0.838 N. It is suspended from a scale, which reads 0.705 N when the piece is submerged in water. What are the volume and density of the piece of metal?
The buoyancy force is 0.838 - 0.705 = 0.133 N
Let D be the density and V be the volume
D*V*g = 0.838 newtons
(1000 kg/m^3)*V*g = 0.133 newtons
(That came from Archimedes principle)
D = 6300 kg/m^3 (or 6.3 g/cm^3)
V = 0.838/(6300 g) = 1.357*10^-5 m^3
= 13.57 cm^3
To find the volume and density of the piece of metal, we need to apply Archimedes' principle. Archimedes' principle 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.
In this case, the weight of the object is given as 0.838 N and the reading on the scale when submerged in water is 0.705 N. The difference between these two readings represents the buoyant force acting on the object.
The buoyant force is equal to the weight of the fluid displaced by the object. Therefore, the buoyant force is equal to the weight of the object in the air (0.838 N) minus the reading on the scale when submerged in water (0.705 N).
Buoyant force = weight of the object - reading on the scale when submerged
Buoyant force = 0.838 N - 0.705 N
Buoyant force = 0.133 N
The buoyant force acting on the object is 0.133 N. This buoyant force is equal to the weight of the water displaced by the object.
Now, to find the volume of the piece of metal, we need to use the equation:
Buoyant force = density of the fluid * volume of the fluid * acceleration due to gravity
The density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2. Converting the buoyant force from newtons to kilograms:
0.133 N = 0.01357 kg × 9.8 m/s^2
Now we can solve for the volume of the object:
Volume = Buoyant force / (density of the fluid * acceleration due to gravity)
Volume = 0.01357 kg × 9.8 m/s^2 / (1000 kg/m^3 * 9.8 m/s^2)
Volume = 0.0013835 m^3
Therefore, the volume of the piece of metal is approximately 0.0013835 cubic meters.
To find the density of the metal, we can use the equation:
Density = Mass / Volume
Mass = weight of the object / acceleration due to gravity
Mass = 0.838 N / 9.8 m/s^2
Mass = 0.0855 kg
Now we can calculate the density:
Density = Mass / Volume
Density = 0.0855 kg / 0.0013835 m^3
Therefore, the density of the piece of metal is approximately 61.83 kg/m^3.