Question

a scuba diver and her gear displace a volume of 65 L and have a total mass of 68kg what is the buoyant force on the diver in sea water? will the diver sink or float?

Answer 1

Answer:

(a)653.6 N

(b) The system will sink

Explanation:

(a)

Assuming the density of sea water as $\rho= 1.025\times 10^{3} Kg/m^{3}$ then considering Archimedes principle  

Upthrust = weight of fluid displaced

Upthrust =Mg = $V\rho g$ (relating density, mass and volume and making mass the subject, mass is a product of density and volume)

Where m is the mass, v is volume in cubic meters and g is acceleration due to gravity.

Substituting 65 l which is 0.065 cubic meters for v, 9.81 for g and density of sea water then

$Upthrust=0.065\times 1025\times 9.81= 653.5913 N$

Rounding off, the buoyancy force= 653.6 N

(b)

The total weight of the diver and gear is given by W=mg

 W= 68x9.81 = 667.08 N

Since weight is greater than the buoyancy, then the system will sink.