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.
130 exam-style questions on Edexcel A Level Maths Applications of Forces, covering 7.1 Static Particles, 7.2 Modelling with Statics, 7.3 Friction and Static Particles, 7.4 Static Rigid Bodies, 7.5 Dynamics and Inclined Planes, and 7.6 Connected Particles 2. Each one has a worked solution and a mark scheme showing where the marks go.