A buoyant force of 26N acts on a piece of metal which us complete immersed in a ethyl alcohol what us tbe volume of the piece if the density of ethanol is 785.06kg m^-3?

Question

Answer

We know that [F(B)]=p(liquid)][V(object)][g]

[26N]=[785.06 kg/m^3]*[V]*[9.8 m/s^2]

[V]=[26 N / 785.06 kg/m^3 * 9.8 m/s^2]

Answer

Analysis of the Problem:
To find the volume of the piece of metal, we need to use the concept of buoyancy. The buoyant force is the force exerted by a fluid on an object immersed in it. It is equal to the weight of the fluid displaced by the object. In this case, the buoyant force acting on the metal is given as 26N. We also know the density of the fluid, which is ethyl alcohol, as 785.06 kg/m³.

Calculations:
To calculate the volume of the metal, we can use the formula for buoyant force:

Buoyant Force = Weight of the Fluid Displaced

The weight of the fluid displaced is equal to the weight of the metal, which is given by the formula:

Weight = Mass × Gravity

Since the volume of the metal is not given, we can assume its density as ρ (rho). Therefore, the mass of the metal can be calculated as:

Mass = Density × Volume

Substituting this into the equation for weight, we get:

Weight = Density × Volume × Gravity

Now, equating the buoyant force to the weight of the fluid displaced, we have:

Buoyant Force = Weight of the Fluid Displaced
26N = Density of Ethanol × Volume of Metal × Gravity

Since we want to find the volume, we can rearrange the equation to solve for it:

Volume of Metal = Buoyant Force / (Density of Ethanol × Gravity)

Final Answer:
Substituting the given values into the equation, we have:

Volume of Metal = 26N / (785.06 kg/m³ × 9.8 m/s²)

Volume of Metal = 0.0034 m³

Therefore, the volume of the piece of metal is 0.0034 cubic meters.

Conclusion:
By using the concept of buoyancy and the given information, we were able to calculate the volume of the metal immersed in ethanol. The volume was found to be 0.0034 cubic meters.

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