Density and fluid pressure：練習問題

A mercury barometer is used to measure atmospheric pressure at sea level. If the barometer is moved to the top of a very high mountain, what happens to the height of the mercury column in the tube?

The diagram below shows a hydraulic press used to lift a load. A force of \( 50 \text{ N} \) is applied to the smaller piston of area \( 0.02 \text{ m}^2 \). Calculate the magnitude of the force exerted by the larger piston, which has an area of \( 0.50 \text{ m}^2 \).

In a hydraulic system, the smaller piston has a cross-sectional area of \( 5.0 \text{ cm}^2 \) and the larger piston has a cross-sectional area of \( 100 \text{ cm}^2 \). If an effort force pushes the smaller piston down by a distance of \( 20 \text{ cm} \), how far does the larger piston move upwards?

The diagram shows a manometer connected to a container of gas. How does the pressure of the gas compare to the atmospheric pressure?

The diagram shows a container of irregular shape filled with water. At which position is the pressure exerted by the water the greatest?

A cylindrical container is filled with a layer of oil (density \( 800 \text{ kg/m}^3 \)) to a depth of \( 0.30 \text{ m} \) floating on top of a layer of water (density \( 1000 \text{ kg/m}^3 \)) that is \( 0.40 \text{ m} \) deep. Calculate the total pressure exerted by the liquids at the bottom of the container, excluding atmospheric pressure. (Take \( g = 10 \text{ m/s}^2 \))

A faulty mercury barometer reads \( 735 \text{ mm} \) when the actual atmospheric pressure is \( 760 \text{ mmHg} \). Calculate the pressure of the air trapped in the space above the mercury column in pascals. (Density of mercury = \( 13600 \text{ kg/m}^3 \), \( g = 10 \text{ m/s}^2 \))

A gas is trapped inside a vertical syringe. A weight of mass \( 2.0 \text{ kg} \) is placed on the plunger, which has a cross-sectional area of \( 4.0 \times 10^{-4} \text{ m}^2 \). If the atmospheric pressure is \( 1.01 \times 10^5 \text{ Pa} \), calculate the total pressure of the trapped gas. (Take \( g = 10 \text{ m/s}^2 \))

A storage tank contains two immiscible liquids: a layer of oil floating on top of a layer of water. The oil has a density of \( 850 \text{ kg/m}^3 \) and a depth of \( 0.60 \text{ m} \). The water has a density of \( 1000 \text{ kg/m}^3 \) and a depth of \( 1.20 \text{ m} \).

(a) Calculate the pressure exerted by the oil at the interface between the oil and the water.
(b) Determine the total pressure at the bottom of the tank, taking the atmospheric pressure to be \( 1.01 \times 10^5 \text{ Pa} \).
(c) If the area of the bottom of the tank is \( 2.5 \text{ m}^2 \), calculate the total downward force acting on the base of the tank. (Take \( g = 10 \text{ m/s}^2 \))

A hydraulic jack uses a lever to apply force to a small piston, which then transmits pressure through an incompressible oil to a large piston. The lever has a pivot at one end. A downward force of \( 40 \text{ N} \) is applied at the handle, which is \( 60 \text{ cm} \) from the pivot. The small piston is located \( 12 \text{ cm} \) from the pivot.

(a) Calculate the downward force exerted by the lever on the small piston.
(b) The small piston has a cross-sectional area of \( 5.0 \times 10^{-4} \text{ m}^2 \). Calculate the pressure created in the oil.
(c) The large piston has a cross-sectional area of \( 0.025 \text{ m}^2 \). Determine the maximum mass that the large piston can lift. (Take \( g = 10 \text{ m/s}^2 \))