In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
A rescue vehicle of mass 1800 kg tows a trailer of mass 600 kg up a straight road inclined at 8° 8°\,8° to the horizontal. The vehicles are joined by a light rigid tow-bar parallel to the road.
While the vehicle's engine is operating, constant resistances of 700 N and 400 N act on the vehicle and trailer respectively, down the road. The system accelerates up the road at 0.600 m s−2^{-2}−2.
Find the driving force produced by the engine.
Find the tension in the tow-bar.
The engine is then switched off while the system is still moving up the road. Assuming the same resistance forces continue to act, find the acceleration of the system and determine whether the tow-bar is in tension or compression.
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.