Answer: -9.63 N
Explanation: Note that vertical pressure is involved in filling the cylinder to the brim with water because filling up a container is done at a downward vertical direction.
Thus, to calculate the downward force of the water, we first calculate the pressure and the area of the base of the cylinder because the force of the water is perpendicular (or normal) to the base of the cylinder and so the magnitude of the force is the product of the pressure of the water and the area of the base of the cylinder.
To compute the vertical pressure, we use the following formula:
[tex]P = \rho gh[/tex]
where
P = vertical pressure of the water (or fluids in general)
[tex]\rho[/tex] = density of the fluid = density of water = [tex]1000 kg/m^3[/tex]
g = gravitational acceleration [tex]\approx 9.81 m/s^2[/tex]
h = height of the cylinder = 50 cm = 0.5 m
So, the pressure is calculated as
[tex]P = \rho gh
\\ = (1000 \text{ kg/m}^3)(9.81 \text{ m/s}^2)(0.5 \text{ m})
\\ \boxed{P = 4905 \text{ Pa}}[/tex]
Now, since the base of the cylinder is a circle, the area of the base cylinder is given by
[tex]\boxed{\text{A} = \frac{\pi d^2}{4}}[/tex]
where
A = Area of the base of the cylinder
d = diameter of the base of the cylinder = 5 cm = 0.05 m
Thus, the area of the base of the cylinder is computed as
[tex]\text{A} = \frac{\pi d^2}{4}
\\
\\ = \frac{\pi (0.05 \text{ m})^2}{4}
\\
\\ \boxed{\text{A} \approx 0.0019634954084\text{ m}^2}[/tex]
Hence, the magnitude of the force F is calculated as
[tex]F = PA
\\ \approx (4905 \text{ Pa})(0.0019634954084\text{ m}^2)
\\ \boxed{F \approx 9.63 \text{ N}}[/tex]
Since, the direction of the force is downward, we put a negative sign. Hence, the downward force is -9.63 N.
