Pressure：練習問題

Which equation is used to calculate the pressure exerted by a solid block on a horizontal surface?

Two containers are filled with different liquids. Container A contains a liquid of density \(800\text{ kg/m}^3\) to a depth of \(25\text{ cm}\). Container B contains a liquid of density \(1000\text{ kg/m}^3\) to a depth of \(20\text{ cm}\).

How does the pressure at the bottom of Container A compare to the pressure at the bottom of Container B?

A simple U-tube manometer contains mercury (density \(13600\text{ kg/m}^3\)). One end is connected to a gas tank and the other end is open to the atmosphere. The mercury level in the arm connected to the tank is \(15.0\text{ cm}\) lower than the level in the open arm.

If the atmospheric pressure is \(760\text{ mm Hg}\), what is the absolute pressure of the gas in the tank?

A force of \(50\text{ N}\) is applied perpendicularly to a surface with an area of \(2.0\text{ m}^2\). What is the pressure exerted on the surface?

A hydraulic jack uses an incompressible liquid to lift a heavy load. The input piston has a radius of \(2.0\text{ cm}\) and the output piston has a radius of \(10\text{ cm}\).

If a force of \(50\text{ N}\) is applied to the input piston, what is the maximum weight that can be lifted by the output piston?

A rectangular wooden block with a base area of \( 0.050\text{ m}^2 \) exerts a force of \( 40\text{ N} \) on a horizontal floor.

Calculate the pressure exerted by the block on the floor.

A cylindrical water tank with a base diameter of \(2.0\text{ m}\) is filled with water to a depth of \(4.5\text{ m}\). The density of water is \(1000\text{ kg/m}^3\).

Calculate the total force exerted by the water on the base of the tank. (Take \(g = 9.8\text{ N/kg}\)).

A container holds a layer of oil (density \(850\text{ kg/m}^3\)) with a thickness of \(0.30\text{ m}\) floating on top of a layer of water (density \(1000\text{ kg/m}^3\)).

Calculate the pressure difference between the top surface of the oil and a point located \(0.20\text{ m}\) below the interface where the oil and water meet. (Take \(g = 9.8\text{ N/kg}\)).

A rectangular metal block has a weight of \(30\text{ N}\). The dimensions of the block are \(0.12\text{ m} \times 0.10\text{ m} \times 0.05\text{ m}\).

(a) Define the term pressure and state the SI unit used for its measurement.
(b) Calculate the maximum pressure that the block can exert when it is placed on a flat horizontal table.
(c) Calculate the minimum pressure that the block can exert on the table.

A vertical cylindrical vessel with a cross-sectional area of \(0.040 \text{ m}^2\) contains a layer of oil floating on a layer of water. The density of the oil is \(800 \text{ kg/m}^3\) and the density of the water is \(1000 \text{ kg/m}^3\). The depth of the oil is \(0.20 \text{ m}\) and the depth of the water is \(0.45 \text{ m}\). A heavy piston of mass \(8.0 \text{ kg}\) is placed inside the cylinder and rests on the top surface of the oil. The atmospheric pressure acting on the piston and the vessel is \(1.0 \times 10^5 \text{ Pa}\). Take the gravitational field strength \(g = 9.8 \text{ N/kg}\).

(a) Calculate the pressure at the interface between the oil and the water layer.

(b) Determine the total pressure acting on the base of the vessel.

(c) At the bottom of the vessel, there is a small circular drain plug with an area of \(5.0 \times 10^{-4} \text{ m}^2\). Calculate the magnitude of the resultant force acting on this plug, considering that the atmospheric pressure acts from the outside.

(d) If the oil layer is replaced with a different liquid that has the same mass but a higher density, explain how the total pressure at the bottom of the vessel would be affected. Assume the piston still rests on top of the new liquid and the vessel remains vertical.