An industrial yard shuttle is used to transport a flatbed loaded with heavy materials along a straight, horizontal track within a factory complex. The shuttle and flatbed are connected by a horizontal, light inextensible coupling.
The mass of the shuttle is 2500 kg2500 \text{ kg}2500 kg. The shuttle's motor generates a constant driving force of 2000 N2000 \text{ N}2000 N, and it experiences a constant resistance of 400 N400 \text{ N}400 N.
The mass of the flatbed is 1500 kg1500 \text{ kg}1500 kg. The flatbed experiences a constant total resistance force of R NR \text{ N}R N.
The assembly moves with a constant acceleration of 0.2 m s−20.2 \text{ m s}^{-2}0.2 m s−2.
(i) Find the value of RRR.
(a) (ii) Determine the tension in the coupling during this motion.
State a modeling assumption you have made regarding the coupling.
While the assembly is moving at a speed of 8 m s−18 \text{ m s}^{-1}8 m s−1, the coupling suddenly fails at point PPP.
The flatbed continues to move forward, subject only to the same resistance force RRR.
The shuttle continues forward but is brought to a stop by its braking system at a distance of 50 m50 \text{ m}50 m from point PPP.
(c) (i) Determine whether the flatbed will collide with the stationary shuttle. Justify your answer with a full calculation.
(c) (ii) Describe how the shuttle's acceleration would change immediately after the coupling fails, assuming the motor's driving force remains constant and the brakes have not yet been applied.
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.