Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A $5\,\text{kg}$ block is on a plane that is inclined at $30^\circ$ to the horizontal, and the coefficient of friction between the block and the plane is $\mu$.
(a)[4]
A force of magnitude $40\,\text{N}$ acts up the plane, parallel to a line of greatest slope, and the block starts to move up the plane (see Fig. 6.1). Show that $\mu < \frac{1}{5}\sqrt{3}$.
(b)[4]
A force of magnitude $40\text{ N}$ is applied horizontally in a vertical plane containing a line of greatest slope, and the block remains at rest (see Fig. 6.2). Show that, correct to $3$ decimal places, the smallest possible value of $\mu$ is $0.152$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Taking components normal to the plane gives $R = 5g\cos 30 = 25\sqrt{3}$” …