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 OCR A Level Maths 3.3 Forces and Newton's Laws, covering 3.3.1 Concept and vector nature of a force, 3.3.2 Newton's first law, 3.3.3 Newton's second law in a straight line, 3.3.4 Newton's second law with vectors (A-level only), 3.3.5 Newton's second law with resolved forces (A-level only), 3.3.6 Weight, 3.3.7 Gravitational acceleration, 3.3.8 Newton's third law, 3.3.9 Normal reaction force, 3.3.10 Smooth contact model, 3.3.11 Equilibrium with connected particles and pulleys, 3.3.12 Newton's third law with resolved forces (A-level only), 3.3.13 Equilibrium by resolving (A-level only), 3.3.14 Equilibrium of forces in two dimensions using vectors (A-level only), 3.3.15 Resolving forces for advanced problems (A-level only), 3.3.16 Resultant forces and components (A-level only), 3.3.17 Dynamics of a particle in a plane (A-level only), 3.3.18 Concept of a frictional force (A-level only), 3.3.19 Contact force components (A-level only), 3.3.20 Coefficient of friction (A-level only), 3.3.21 Static and limiting equilibrium on a rough surface (A-level only), 3.3.22 Motion of a body on a rough surface (A-level only), and 3.3 Forces and Newton's Laws. Each one has a worked solution and a mark scheme showing where the marks go.