An Antarctic rescue system consists of a lead snowmobile and a medical sled connected by a light, rigid coupling rod. The snowmobile has a mass of 50 kg and the medical sled has a mass of 30 kg. A driving force is provided by a winch cable attached to the front of the snowmobile, exerting a tension of 120 N at an angle of 25∘ 25^\circ\,25∘ above the horizontal. The system accelerates forward from rest across a level ice field at a constant rate of 0.6 m s-2.
The snowmobile experiences a constant resistance to motion of 45 N.
Show that the resistance force acting on the medical sled is approximately 15.8 N.
At the instant the system attains a speed of 1.5 m s-1, the winch cable snaps. (i) Assuming the resistance forces on both the snowmobile and the sled remain constant, determine the magnitude of the thrust in the coupling rod while the system is decelerating. (ii) Calculate the distance, ddd, that the system slides from the moment the cable snaps until it comes to a complete halt.
State one modelling assumption you have made about 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.