A sled of weight 50 N is held on a rough hill inclined at an angle of 45∘ 45^\circ\,45∘ to the horizontal. A rope pulls the sled up the hill with a force of 60 N, and the sled is in equilibrium on the point of slipping up the hill.
Find the coefficient of friction between the sled and the hill.
The 60 N force is removed. Determine whether or not the sled moves.
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.