Physics 9702 · AS & A Level · Density and pressure
Density and pressure — practice question
A cube with sides of length $5.1\,\text{cm}$ and weight $4.0\,\text{N}$ is tied to the lower end of a vertical spring, while the other end of the spring is fixed to a point above. When the cube is released, it moves down into the water as the spring lengthens. It settles at equilibrium with its base $7.0\,\text{cm}$ beneath the water surface. The density of the water is $1000\,\text{kg m}^{-3}$.
(a)[2]
Calculate the pressure difference between the water acting on the cube's bottom face and the water acting on its top face.
(b)[2]
Use your answer in (a) to demonstrate that the upthrust on the cube is $1.3\,\text{N}$.
(c)[1]
Calculate the force exerted on the spring by the cube when the cube is in equilibrium in the water.
(d)[3]
The spring follows Hooke’s law and has a spring constant of $30\,\text{N m}^{-1}$. Determine the initial height above the water surface of the base of the cube before release.
(e(i))[2]
The cube in the water is released from the spring. Determine the cube's initial acceleration.
(e(ii))[2]
Describe and explain how the acceleration of the cube changes, if at all, as it sinks in the water.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $p = 1000 \times 9.81 \times (7.0 \times 10^{-2}$ or $1.9 \times 10^{-2})$.” …