Quick questions on Forces and Newton's laws: F equals ma, resolving forces and friction - Edexcel A-Level Maths

Newton's first law says a body stays at rest or moves at constant velocity unless a resultant force acts. The third law says that if body $A$ exerts a force on body $B$, then $B$ exerts an equal and opposite force on $A$.

Forces are resolved into perpendicular components, often horizontal and vertical or along and perpendicular to a slope. The body is in equilibrium when the resultant in each direction is zero, and accelerates when there is a non-zero resultant.

The same routine handles almost every Edexcel forces question. First, draw a clear diagram and mark every force: weight $mg$ downward, the normal reaction $R$ perpendicular to the surface, any applied force, tension along strings, and friction opposing the direction of (attempted) motion. Second, choose convenient perpendicular directions to resolve in. On a slope it is almost always cleanest to use along-the-slope and perpendicular-to-the-slope rather than horizontal and vertical.

A light inextensible string over a smooth pulley has the same tension throughout.

A force of $12$ N acts on a $3$ kg mass on a smooth surface. Find the acceleration. [2 marks]

A $5$ kg block on a rough horizontal surface has $\mu = 0.4$. Find the maximum friction. Take $g = 9.8$.