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Feb/Mar 2023 p42 q4
3440
A toy railway locomotive of mass 0.8 kg is towing a truck of mass 0.4 kg on a straight horizontal track at a constant speed of 2 m s-1. There is a constant resistance force of magnitude 0.2 N on the locomotive, but no resistance force on the truck. There is a light rigid horizontal coupling connecting the locomotive and the truck.
(a) State the tension in the coupling.
(b) Find the power produced by the locomotive’s engine.
The power produced by the locomotive’s engine is now changed to 1.2 W.
(c) Find the magnitude of the tension in the coupling at the instant that the locomotive begins to accelerate.
Solution
(a) Since the locomotive and truck are moving at a constant speed, the net force is zero. Therefore, the tension in the coupling is 0 N.
(b) The power produced by the locomotive's engine is given by the formula \(P = Fv\), where \(F\) is the force and \(v\) is the velocity. The resistance force is 0.2 N, and the velocity is 2 m/s. Thus, \(P = 0.2 \times 2 = 0.4 \text{ W}\).
(c) When the power is changed to 1.2 W, the driving force \(DF\) is \(\frac{1.2}{2} = 0.6 \text{ N}\). Using Newton's second law for the locomotive: \(DF - 0.2 - T = 0.8a\). For the truck: \(T = 0.4a\). For the system: \(DF - 0.2 = 1.2a\). Solving these equations gives \(T = \frac{2}{15} \text{ N}\).