Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A force with magnitude $F\,\text{N}$ lies in a horizontal plane and has components $27.5\,\text{N}$ and $-24\,\text{N}$ along the $x$-axis and the $y$-axis respectively. The force is directed at an angle of $\alpha^\circ$ below the $x$-axis.
(i)[4]

Determine the values of $F$ and $\alpha$.

(ii)[3]

A second force, with magnitude $87.6\,\text{N}$, lies in the same plane and is $90^\circ$ anticlockwise from the force of magnitude $F\,\text{N}$. The resultant of the two forces has magnitude $R\,\text{N}$ and forms an angle of $\theta^\circ$ with the positive $x$-axis. Determine the values of $R$ and $\theta$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $F^2 = X^2 + Y^2 = 27.5^2 + (-24)^2$” …

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