Question

A solid rock, suspended in air by a spring scale, has a

measured mass of 9.00 kg. When the rock is completly
submerged under water, the scale reads 3.00 kg.
a) Find the magnitude of the buoyant force and
b) What is the volume of the rock?
(water density = 1 000 kg/m³) what is the answer

Answer 1

a. 58.8 N.

b. 6 * 10⁻³m³ or 6cm³.

Step-by-step explanation:

a) Find the magnitude of the buoyant force.

Buoyant force is the force that a liquid applies into an object that is partially or totally submerged into it.

In this case, the buoyant force is given by the differente between the weight (in Newtons) of the rock in the air and the weight (in Newtons) of the rock while submerged in water.

Therefore:

Buoyant force: Fb= (9.00kg * 9.8m/s²) - (3.00kg * 9.8m/s²)= (88.2 N) - (29.4 N)= 58.8 N.

b) What is the volume of the rock? (water density = 1 000 kg/m³).

The Principle of Archimedes states the following: "A body immersed in a fluid experiences an upthrust equal to the weight of the fluid displaced".

This can be expressed in a mathematical equation in the following fashion:

`Fb=dgv`, where d is the density of the liquid; g is the acceleration of gravity, and v is the volume of the part of the body that is submerged.

In this case, the rock is totally submerged, hence, v is the total volume is the rock.

Taking into account that we have all the needed variables of this equation, except for the volume, we can solve the equation for v and calculate it's value. This is the process:

`Fb=dgv\\\\v=(Fb)/(dg) \\\\v=(58.8 N)/((1 000 kg/m^(3) )(9.8m/s^(2) ))\\\\v=0.006m^(3)=6*10^(-3) m^(3)`

Now, in order to give a more reaader friendly result, we may convert the volume from cubic meters to cubic certimeters by multiplying by 10³:

`6*10^(-3) *10^(3) m^(3)=6cm^(3)`