A heavy-duty mining shuttle system consists of a power-lead unit of mass 1500 kg and an ore sled of mass 2500 kg, connected by a light, rigid coupling rod. The entire shuttle is pulled forward along a horizontal track by an overhead haulage cable attached to the front of the power-lead unit. The cable is inclined at an angle of 25∘ 25^\circ\,25∘ to the horizontal and exerts a constant tension of 24,000 N. The system accelerates from rest at a constant rate of 1.2 m s-2.
The power-lead unit experiences a constant resistance to motion of 8000 N.
Show that the resistance to motion experienced by the ore sled is approximately 8950 N.
At the instant the shuttle reaches a velocity of 6 m s-1, the haulage cable suddenly snaps. (i) Assuming the resistance forces on both units remain unchanged, calculate the tension (or thrust) in the coupling rod during the subsequent deceleration.
(ii) Determine the total distance, ddd, the shuttle travels from the moment the cable snaps until it comes to a complete halt.
State one modelling assumption you have made concerning the coupling rod.
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.