Density and pressure：練習問題

A rectangular block has a mass of \(400 \text{ g}\) and dimensions \(10.0 \text{ cm} \times 5.0 \text{ cm} \times 2.0 \text{ cm}\). What is the maximum pressure it can exert on a horizontal surface?

A solid uniform cube of side length \(2.0 \text{ cm}\) and mass \(40 \text{ g}\) rests on a horizontal surface. What is the pressure exerted by the cube on the surface? (Take \(g = 9.81 \text{ m s}^{-2}\))

A rectangular swimming pool contains water of density \( 1000 \text{ kg m}^{-3} \). The pool has a depth of \( 2.5 \text{ m} \). Calculate the pressure exerted by the water at the bottom of the pool. (Take \( g = 9.81 \text{ m s}^{-2} \))

A research submarine is at a depth of \(150 \text{ m}\) in the ocean. Taking the density of seawater as \(1030 \text{ kg m}^{-3}\) and \(g = 9.81 \text{ m s}^{-2}\), calculate the pressure exerted by the water on the submarine.

A solid cube of side length \( 0.20 \, \text{m} \) has a mass of \( 64 \, \text{kg} \). Calculate the density of the cube in \( \text{kg m}^{-3} \).

A hollow cylindrical buoy of mass \( 450 \text{ kg} \) and cross-sectional area \( 1.2 \text{ m}^2 \) floats in seawater of density \( 1030 \text{ kg m}^{-3} \). The buoy is held in equilibrium by a cable attached to the seabed.

(a) Calculate the upthrust acting on the buoy when it is submerged to a depth where the volume of displaced water is \( 0.85 \text{ m}^3 \). [2]

(b) By considering the forces acting on the buoy, calculate the tension in the cable when it is submerged to the depth described in part (a). [2]

(c) The cable snaps, and the buoy begins to rise. At a particular instant, its upward velocity is \( 1.5 \text{ m s}^{-1} \). The drag force \( D \) on the buoy is given by \( D = 0.5 \rho A v^2 \), where \( \rho \) is the density of water, \( A \) is the cross-sectional area, and \( v \) is the velocity. Calculate the net upward acceleration of the buoy at this instant. [4]