A 50,000 kg locomotive is traveling at 10 m/s when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop? Assume the track is level.

Question

doc.brown · Answer

The train has no force accelerating it as the engine has failed.  The only thing that will slow the train down are other forces, like air resistance, friction, and the x component of gravity (if the train starts up a hill).  Without these forces, the train will roll forever.

Do you have values for air resistance, or friction?

anonymous · Answer

no, but I would think that steel on steel coefficient of friction is available for everyone to look it up. http://www.tribology-abc.com/abc/cof.htm

doc.brown · Answer

$$F_{fr}=\mu_{k}F_{N}=\mu_{k}mg$$$$0.5(50000kg)(-9.8\frac{m}{s^{2}})$$$$=-245000N$$
$$a=F/m$$$$-245000N/50000kg$$$$=-4.9\frac{m}{s^{2}}$$$$t = \frac{v-v_{0}}{a}$$$$\frac{0-10\frac{m}{s}}{-4.9\frac{m}{s^{2}}}$$$$=2s$$