Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
Masses $A$ and $B$, with masses $1.2\,\text{kg}$ and $2.0\,\text{kg}$ respectively, are fixed to the two ends of a light inextensible string that passes over a fixed smooth pulley. $A$ is kept at rest while $B$ hangs freely, and both vertical sections of the string are straight. When $A$ is released, it moves upwards. In the later motion, it does not reach the pulley.
(i)[4]
Determine the acceleration of $A$ and the tension in the string.
(ii(a))[3]
Increase in $A$’s potential energy during the first $1.5\,\text{m}$ of $A$’s motion.
(ii(b))[3]
Work done on $A$ by the tension in the string.
(ii(c))[3]
Increase in $A$’s kinetic energy.
(iii)[4]
$B$ reaches the floor $1.6\,\text{s}$ after $A$ is released. $B$ stops without bouncing and the string goes slack. Find the interval from the moment the string becomes slack until it becomes taut again.
Worked solution & mark scheme
This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to obtain equations $T - 12 = 1.2a$ and $20 - T = 2a$ (or equivalent)” …