Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
Particles $A$ and $B$, with masses $m\text{ kg}$ and $4\text{ kg}$ respectively, are joined by a light inextensible string which runs over a fixed smooth pulley. $A$ rests on a rough fixed slope inclined at $30^{\circ}$ to the horizontal ground. $B$ is suspended vertically beneath the pulley and lies $0.5\text{ m}$ above the ground (see diagram). The coefficient of friction between the slope and $A$ is $0.2$.
(i)[6]
Assuming the system is in equilibrium and particle $A$ is just about to move directly up the slope, show that $m = 5.94$, correct to $3$ significant figures.
(ii)[8]
When $m = 3$, the system is released from rest with the string taut. Determine the total distance travelled by $A$ before it comes to instantaneous rest. You may assume that $A$ does not reach the pulley.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The normal reaction is $R=mg\cos30$” …