An electric monorail cargo shuttle of total mass 1.6×104 kg1.6 \times 10^4 \text{ kg}1.6×104 kg operates in an underground transport tunnel. Power is supplied by a high-voltage third rail at a potential of +15 kV+15 \text{ kV}+15 kV relative to earthed tracks at 0 kV0 \text{ kV}0 kV.
The shuttle starts from rest. The forward tractive force FFF is constant at 12.5 kN12.5 \text{ kN}12.5 kN for speeds less than 4.0 m s−14.0 \text{ m s}^{-1}4.0 m s−1.
Show that the shuttle's acceleration is approximately 0.8 m s−20.8 \text{ m s}^{-2}0.8 m s−2.
Calculate the distance sss that the shuttle travels from rest to reach a speed of 4.0 m s−14.0 \text{ m s}^{-1}4.0 m s−1.
The speed of the shuttle is vvv. During one phase of its route, the shuttle accelerates from v=15 m s−1v = 15 \text{ m s}^{-1}v=15 m s−1 to v=30 m s−1v = 30 \text{ m s}^{-1}v=30 m s−1. The graph of tractive force FFF against speed vvv for this phase is shown below.
Use the graph to show that the output power of the electric motor during this phase is constant at about 0.45 MW0.45 \text{ MW}0.45 MW.
Calculate the current III drawn by the electric motor when the shuttle is travelling at 22.5 m s−122.5 \text{ m s}^{-1}22.5 m s−1.
The overhead supply line for the shuttle system is constructed from several equal lengths of a modern high-conductivity alloy wire. Some technical data for one standard length of this wire are shown below:
- length = 850 m850 \text{ m}850 m
- area of cross-section = 1.5×10−4 m21.5 \times 10^{-4} \text{ m}^21.5×10−4 m2
- resistivity = 2.4×10−8 Ω m2.4 \times 10^{-8} \ \Omega \text{ m}2.4×10−8 Ω m
- the Young modulus = 9.6×1010 Pa9.6 \times 10^{10} \text{ Pa}9.6×1010 Pa
- strain = 1.5%1.5\%1.5%
Calculate the resistance RRR of one length of this wire.
Calculate the tension TTT in one length of this wire.