Challenging +1.2 This is a standard Further Mechanics work-energy problem requiring application of the work-energy principle to motion on a rough inclined plane. While it involves multiple forces (applied force, friction, weight component) and requires careful bookkeeping of energy terms, the method is straightforward once set up. The constraint that the applied force is constant but unspecified creates an inequality to solve, adding modest problem-solving demand beyond routine exercises. Typical of Further Mechanics content, making it moderately above average difficulty.
4 A block of mass 20 kg is placed on a rough plane inclined at an angle \(30 ^ { \circ }\) to the horizontal. The block is pulled up the plane by a constant force acting parallel to a line of greatest slope.
The block passes through points A and B on the plane with speeds \(9 \mathrm {~ms} ^ { - 1 }\) and \(4 \mathrm {~ms} ^ { - 1 }\) respectively with B higher up the plane than A . The distance between A and B is \(x \mathrm {~m}\) and the coefficient of friction between the block and the plane is \(\frac { \sqrt { 3 } } { 49 }\).
Use an energy method to determine the range of possible values of \(x\).
4 A block of mass 20 kg is placed on a rough plane inclined at an angle $30 ^ { \circ }$ to the horizontal. The block is pulled up the plane by a constant force acting parallel to a line of greatest slope.\\
The block passes through points A and B on the plane with speeds $9 \mathrm {~ms} ^ { - 1 }$ and $4 \mathrm {~ms} ^ { - 1 }$ respectively with B higher up the plane than A . The distance between A and B is $x \mathrm {~m}$ and the coefficient of friction between the block and the plane is $\frac { \sqrt { 3 } } { 49 }$.
Use an energy method to determine the range of possible values of $x$.
\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2020 Q4 [8]}}