Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
Particle $P$, with mass $0.3\,\text{kg}$, is stationary on a rough plane that makes an angle $\theta$ with the horizontal, where $\sin\theta = \frac{7}{25}$. A force of magnitude $4\,\text{N}$, applied horizontally in the vertical plane containing a line of greatest slope of the plane, acts on $P$ (see diagram). The particle is on the point of moving up the plane.
(a)[4]
Show that the coefficient of friction between the particle and the plane has value $\frac{3}{4}$.
(b)[3]
The horizontal force is replaced by a force of magnitude $4\,\text{N}$ acting up the plane parallel to a line of greatest slope. Find the acceleration of $P$.
(c)[3]
With $P$ initially at rest, a force of $4\,\text{N}$ parallel to the plane acts for $3$ seconds and is then removed. Find the total distance travelled until $P$ comes to instantaneous rest.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolving the forces gives correct equations for $R$ and $F$” …