Standard +0.3 This is a standard two-equation mechanics problem requiring resolution of forces in limiting equilibrium in both directions. While it involves simultaneous equations and careful handling of friction direction reversal, it follows a well-established textbook method with no novel insight required. Slightly easier than average due to its routine nature.
5 A particle of mass \(m \mathrm {~kg}\) is resting on a rough plane inclined at \(30 ^ { \circ }\) to the horizontal. A force of magnitude 10 N applied to the particle up a line of greatest slope of the plane is just sufficient to stop the particle sliding down the plane. When a force of 75 N is applied to the particle up a line of greatest slope of the plane, the particle is on the point of sliding up the plane. Find \(m\) and the coefficient of friction between the particle and the plane.
5 A particle of mass $m \mathrm {~kg}$ is resting on a rough plane inclined at $30 ^ { \circ }$ to the horizontal. A force of magnitude 10 N applied to the particle up a line of greatest slope of the plane is just sufficient to stop the particle sliding down the plane. When a force of 75 N is applied to the particle up a line of greatest slope of the plane, the particle is on the point of sliding up the plane. Find $m$ and the coefficient of friction between the particle and the plane.
\hfill \mbox{\textit{CAIE M1 2016 Q5 [6]}}