Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
Three coplanar forces act at a point. Their magnitudes are $20\,\text{N}$, $25\,\text{N}$ and $30\,\text{N}$, and their directions are indicated in the diagram, where $\sin\alpha = 0.28$ and $\cos\alpha = 0.96$, and $\sin\beta = 0.6$ and $\cos\beta = 0.8$.
(i)[2]
Show that the resultant of the three forces has no component in the $x$-direction.
(ii)[2]
Determine the magnitude and direction of the resultant of the three forces.
(iii)[1]
A force of magnitude $20\,\text{N}$ is replaced by another force. This leaves the resultant force unchanged in magnitude but opposite in direction. State the magnitude and direction of the replacement force.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “After resolving in the $x$-direction, $X = 25 \times 0.96 - 30 \times 0.8 = 0$” …