An automated electric cargo shuttle of mass 15000 kg15000\text{ kg}15000 kg operates with a constant power output of 120 kW120\text{ kW}120 kW and can achieve a maximum speed of 20 m s−120\text{ m s}^{-1}20 m s−1 on flat, horizontal guide-rails. The maximum kinetic energy of the shuttle is 3.0 MJ3.0\text{ MJ}3.0 MJ.
The shuttle is initially at rest on long horizontal rails. Show that the minimum time taken for the shuttle to reach its maximum speed is 25 s25\text{ s}25 s.
The shuttle is moving along the horizontal rails at its constant maximum speed of 20 m s−120\text{ m s}^{-1}20 m s−1. The weight of the shuttle is WWW, the total normal contact force from the rails is NNN, and the driving force propelling the shuttle is FFF to the right.
Complete the free body diagram for the shuttle by identifying and describing the missing force, and calculate the magnitudes of all four forces.
While travelling at 20 m s−120\text{ m s}^{-1}20 m s−1, the shuttle's collision avoidance system detects a stationary obstacle 90 m90\text{ m}90 m directly ahead. The drive power is immediately shut off and the emergency mechanical brakes are engaged. The constant braking force opposing motion is 40 kN40\text{ kN}40 kN. The system processing and actuator response time is 0.40 s0.40\text{ s}0.40 s.
Show with the help of calculations that the shuttle will stop before reaching the obstacle.
