Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
Masses $3m$ kg and $2m$ kg, named $A$ and $B$, are fixed to the two ends of a light inextensible string. The string runs over a fixed smooth pulley that is attached to the edge of a plane. The plane makes an angle $\theta$ with the horizontal. $A$ is on the plane while $B$ hangs vertically, $0.8$ m above the floor. The section of string from $A$ to the pulley is parallel to a line of greatest slope on the plane (see diagram). At the beginning, both $A$ and $B$ are at rest.
(a)[3]
Because the plane is smooth, determine the value of $\theta$ that keeps $A$ at rest.
(b)[5]
Now the plane is rough, $\theta = 30\degree$ and the acceleration of $A$ up the plane is $0.1$ m s$^{-2}$. Show that the coefficient of friction between $A$ and the plane is $\frac{1}{10}\sqrt{3}$.
(c)[4]
Once $B$ reaches the floor, it stops. Determine the time after $B$ reaches the floor during which $A$ continues to move up the plane. You may assume that $A$ does not reach the pulley.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hence, $T - 2mg = 0$” …