Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A particle with mass $0.3\,\text{kg}$ is let go from rest above a tank of water. It moves straight down and takes $0.8\,\text{s}$ to arrive at the water surface. Its speed does not change suddenly as it enters the water. The water depth in the tank is $1.25\,\text{m}$. A force from the water acts on the particle and opposes its motion. The work done against this resisting force from the moment the particle enters the water until it reaches the tank bottom is $1.2\,\text{J}$. On reaching the bottom, it rebounds vertically upwards with initial speed $7\,\text{m s}^{-1}$. While moving up through the water, it is acted on by a constant resistance force of $1.8\,\text{N}$. The particle is instantaneously at rest $t$ seconds after rebounding from the bottom of the tank.
(i)[4]
Apply an energy method to determine the particle’s speed when it reaches the tank bottom.
(ii)[7]
Determine the value of $t$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Speed at the liquid surface from motion or energy: $v=8$” …