A rough ramp is inclined to the horizontal at an angle α\alphaα, where tanα=34\displaystyle \tan \alpha = \frac{3}{4}tanα=43. A box of mass M M\,M kg is placed on the ramp and released from rest. The coefficient of friction between the box and the ramp is 12\displaystyle \frac{1}{2}21.
Find the acceleration of the box as it slides down the ramp.
A different box with mass 3M 3M\,3M kg is placed on the same ramp. Explain how the acceleration of this box would compare to your answer in part (a).
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.