Question bank: Hydrostatics: Stevin's Theorem

Stevin's Theorem is an important mathematical principle that deals with the infinite sum of the harmonic series, being mainly used to calculate various types of physical quantities based on measurements obtained through experiments. When calculating the average scalar velocity of an object in MRUV, it is possible to use the following formula: v = Δs/Δt. Which of the alternatives below is correct?

Explain what the Stevin's Theorem is and present two practical applications of this theorem in everyday situations. Then, calculate the pressure exerted by a liquid at a point located 4 meters deep, knowing that the density of the liquid is 1.2 g/cm³ and that the atmospheric pressure is 1 atm. Show all your reasoning.

A physics student is designing an experiment and wants to apply the Stevin's Theorem to calculate the pressure at point P in a water column present in a U-shaped tube, with a height of 5 meters and a liquid density of 1000 kg/m³. The atmospheric pressure at the location is 101325 Pa. Determine the pressure at point P, considering it is 3 meters deep relative to the water surface.

A rectangular aquarium has a length of 50cm, a width of 40cm, and a height of 40cm. It is completely filled with a liquid with a density of 1000 kg/m³. The external side of the aquarium has an opening in the shape of a small hole, which is located 20cm from the base of the aquarium. Considering the Stevin's Theorem and the standard atmosphere, calculate: a) the absolute pressure at the hole; b) the liquid's exit velocity through the hole; c) the horizontal distance that the liquid jet reaches from the hole until it reaches the same initial height.

A wooden block with a density of 600 kg/m^3 and a volume of 0.02 m^3 is submerged in a container containing water, which has a density of 1000 kg/m^3. The wooden block is connected by a wire to a scale resting at the bottom of the container. The wire exerts a force that is transmitted to the scale. Considering the acceleration due to gravity as g = 10 m/s^2, calculate the reading on the scale. Assume that the scale is calibrated to measure the force correctly and that there are no currents inside the container that could affect the scale reading. Explain how the scale reading is related to the Stevin's Theorem and the pressure exerted by the wooden block on the water.