Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

A particle $P$ with mass $0.2\text{ kg}$ is released from rest at a point $7.2\text{ m}$ above the liquid surface in a container. $P$ drops through the air and then enters the liquid. Air resistance is absent and there is no sudden change in speed as $P$ enters the liquid. When $P$ is $0.8\text{ m}$ below the surface of the liquid, $P$’s speed is $6\,\text{m s}^{-1}$. The only force on $P$ from the liquid is a constant resistance to motion of magnitude $R\text{ N}$. The liquid has depth $3.6\text{ m}$ in the container. $P$ is removed from the container and attached to one end of a light inextensible string. $P$ is placed at the bottom of the container and then pulled vertically upwards with constant acceleration. The resistance to motion of $R\text{ N}$ continues to act. The particle reaches the surface $4\text{ s}$ after leaving the bottom of the container.
(i)[5]

Determine the deceleration of $P$ as it falls through the liquid, and hence determine the value of $R$.

(ii)[4]

Determine the tension in the string.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use $v^2 = 2gs$ to determine the speed at the surface, $v = 12\text{ m s}^{-1}$

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