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.
