A winch system used for lifting geologic samples from a crater consists of a sample sled, AAA, and a counterweight, BBB, connected by a light inextensible cable. Sled A A\,A has a mass of 30 kg and counterweight B B\,B has a mass of 50 kg.
Sled A A\,A is positioned on a rough track inclined at 60∘ 60^\circ\,60∘ to the horizontal. The cable passes over a smooth pulley at the top of the track, and counterweight B B\,B hangs freely. The system is released from rest with the cable taut and parallel to the line of greatest slope. Counterweight B B\,B descends with acceleration a a\,a m s−2^{-2}−2 and the tension in the cable is T T\,T Newtons.
Explain why the equation of motion for counterweight B B\,B is 50g−T=50a50g - T = 50a50g−T=50a.
Show that the normal reaction force, RRR, between sled A A\,A and the track is 15g Newtons.
The coefficient of friction, μ\muμ, between sled A A\,A and the track satisfies 0≤μ≤0.20 \le \mu \le 0.20≤μ≤0.2. Show that
a≥(47−153)g80 a \ge \frac{(47 - 15\sqrt{3})g}{80} a≥80(47−153)gState one modelling assumption used in this problem regarding the cable or pulley.
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.