Resolving forces and resultantsAQA A-Level Maths: Mind map

Exam questions on Resolving forces and resultants

1. Three coplanar forces $\mathbf{P}=(4\mathbf{i}-3\mathbf{j})$ N, $\mathbf{Q}=(-7\mathbf{i}+5\mathbf{j})$ N and $\mathbf{R}$ act on a particle, which is in equilibrium. The vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
   Find the angle that $\mathbf{R}$ makes with the direction of $\mathbf{i}$, and state whether it is above or below that direction.2 marks
2. A block of mass $6$ kg is released from rest on a smooth plane inclined at $30^\circ$ to the horizontal. Model the block as a particle, with $g=9.8\ \text{m s}^{-2}$.
   Find the acceleration of the block down the plane.2 marks
3. Two horizontal forces $(6\mathbf{i}+4\mathbf{j})$ N and $(-2\mathbf{i}+8\mathbf{j})$ N act on a particle of mass $2$ kg on a smooth horizontal surface, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular horizontal unit vectors. These are the only horizontal forces. The particle starts from rest at the origin $O$.
   Find the acceleration of the particle as a vector, and its magnitude.3 marks