Answer:
[tex]P = 1.090\,N[/tex]
Explanation:
The constant speed means that ball is not experimenting acceleration. This elements is modelled by using the following equation of equilibrium:
[tex]\Sigma F = P - W + F_{D}[/tex]
[tex]\Sigma F = P - \rho \cdot V \cdot g + c\cdot v = 0[/tex]
Now, the exerted force is:
[tex]P = \rho \cdot V \cdot g - c\cdot v[/tex]
The volume of a sphere is:
[tex]V = \frac{4\cdot \pi}{3}\cdot R^{3}[/tex]
[tex]V = \frac{4\cdot \pi}{3}\cdot (0.014\,m)^{3}[/tex]
[tex]V = 1.149\times 10^{-5}\,m^{3}[/tex]
Lastly, the force is calculated:
[tex]P = (8910\,\frac{kg}{m^{3}} )\cdot (1.149\cdot 10^{-5}\,m^{3})\cdot (9.81\,\frac{m}{s^{2}} )+(0.950\,\frac{kg}{s})\cdot (0.09\,\frac{m}{s} )[/tex]
[tex]P = 1.090\,N[/tex]
