The train shown below is traveling down a 10degree grade when the driver sees a

Question

The train shown below is traveling down a 10degree grade when the driver sees a bowl of ice cream on the track ahead. The driver locks the wheels of the engine in the position shown. If the train was moving at 20 m/s before the engine wheels locked, how much time will it take for the train to stop after the brakes are applied? Also, what is the force in the coupling between the engine and the cheap wine car? The kinetic friction coefficient between the wheels and the rails is 0.4. Mass of Engine: 40 Mg Mass of Cheap Wine: 10 Mg Mass of Mattas: 10 Mg

Explanation / Answer

First step is to draw your forces on the picture.
for the forces parallel to the surface, you can find the deceleration of the whole thing to be -

-N+(m1+m2+m3)gcos10=-(m1+m2+m3)a

where N can be found from the perpendicular forces to the surface, which is

N-(m1+m2+m3)sin10=0

once you find a, the kinamatic equation

vf=vi+at

where vf is 0 and vi is 20m/s and you know a

for the force, you can cut around the engine and the rod connecting both can be a force F

the equation is -F-N+mgcos10=-ma

and solve for F

I hope this helps, if not please ignore

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