A piece of aluminum is attached to a string and suspended in a pool of oil with density 780 kg/m3. If the apparent weight of the aluminum is 590 N, what is the volume of the aluminum?
To find the volume of the aluminum, we will use the concept of buoyancy.
The buoyant force acting on the aluminum is equal to the weight of the fluid displaced by the aluminum. This can be calculated using the formula:
Buoyant force (Fb) = Density of fluid (ρf) * Volume of fluid displaced (Vf) * Acceleration due to gravity (g)
In this case, the buoyant force is equal to the apparent weight of the aluminum, which is given as 590 N, and the density of the fluid is 780 kg/m3. The acceleration due to gravity is approximately 9.8 m/s2.
So, we can rearrange the formula to solve for the volume of the fluid displaced:
Vf = Fb / (ρf * g)
Substituting the given values:
Vf = 590 N / (780 kg/m3 * 9.8 m/s2)
Now, we can calculate the volume of the fluid displaced:
Vf = 0.076 m3
Since the aluminum is fully submerged in the fluid, the volume of the aluminum is equal to the volume of the fluid displaced.
Therefore, the volume of the aluminum is 0.076 m3.
To find the volume of the aluminum, we need to understand the concept of buoyancy.
Buoyancy is the upward force exerted by a fluid (in this case, oil) on an object immersed in it. It is equal to the weight of the fluid displaced by the object.
In this problem, the apparent weight of the aluminum is given as 590 N. The apparent weight is the actual weight of an object minus the buoyant force acting on it.
Given that the density of the oil is 780 kg/m^3, we can use the density of the fluid to find the buoyant force on the aluminum.
The buoyant force is calculated using the formula:
Buoyant force = density of fluid × volume of fluid displaced × acceleration due to gravity
Since the aluminum is fully submerged, the volume of fluid displaced is equal to the volume of the aluminum.
Let's denote the volume of the aluminum as V.
Now, we can equate the buoyant force to the apparent weight of the aluminum:
Buoyant force = Apparent weight
density of fluid × V × g = 590 N
Solving for V, the volume of the aluminum:
V = (Apparent weight) / (density of fluid × g)
Substituting the known values:
V = 590 N / (780 kg/m^3 × 9.8 m/s^2)
Calculating the volume:
V ≈ 0.076 m^3
Therefore, the volume of the aluminum is approximately 0.076 cubic meters.