A-Level Mathematics: Dynamics and Inclined Planes questions

B1: $\\mu mg\cosθ$. Accept: equivalent notation for limiting friction on the plane. Do not award for $mg\sin\\theta$, which is the component of weight down the plane, or for $mg\cos\\theta$, which is the normal reaction without friction.

B1: Resolve the weight $2g$ into components and use $2g \sin 30^\circ$. A1: $g$. Accept $2g \times$\frac{1}{2}$= g$. Do not award for using $2g \cos 30^\circ$ or for omitting the mass factor.

M1: Resolves forces parallel to the plane and includes both the component of weight $2g\sin 30^\circ$ and friction $\\mu R$ acting down the plane. M1: Uses $R=2g\cos 30^\circ$ and hence a constant deceleration, or sets up $v{^2}=u{^2}+2as$ with correct sign convention. M1: Forms the equation $0=6{^2}+2as$ with $a$ found from the net retarding force, or an equivalent energy/motion equation. A1: Correct acceleration or retarding force leading to $s=\frac{36}{2a}$. A1: $1.8\,\text{m}$. Accept $1.79\,\text{m}$ to $1.80\,\text{m}$ if rounded from a correct exact setup. Do not award for using $\sin 30^\circ$ and $\cos 30^\circ$ the wrong way round, for friction acting up the plane, or for omitting friction entirely.