Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A box with mass $8\text{ kg}$ rests on a rough plane that is tilted at $5^\circ$ to the horizontal. A force of size $P\text{ N}$ is applied to the box, directed upwards and parallel to the line of greatest slope of the plane. For $P = 7X$, the box travels up the line of greatest slope with acceleration $0.15\text{ m s}^{-2}$, whereas for $P = 8X$, it travels up the line of greatest slope with acceleration $1.15\text{ m s}^{-2}$.
(main)[8]

Determine $X$ and the coefficient of friction between the box and the plane.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply Newton’s 2nd law in the form $P - 8g\sin5^\circ - F = 8a$

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