You have been hired to investigate a railroad accident. One night, a 3300 kg rai

Question

You have been hired to investigate a railroad accident. One night, a 3300 kg railroad car was left parked on top of a hill, while a second 3300 kg car was standing down below, as shown in figure. In the morning, both cars are found coupled together in the lake. ( The tracks extend right to the shore, to facilitate loading boats with ore.) The company accuses the engineer of forgetting to set the brake on the upper car, so that during the night it rolled down, hit, and coupled to the lower car, and its momentum carried both into the lake. The engineer denies this, saying that someone must have released the brake and pushed the upper car. Can you use physics to determine whether the engineer is correct?

Explanation / Answer

If no one pushed the upper car, its initial velocity is zero.

velocity of upper before coupling with bottom car,

v1 = sqrt(2*g*h1)

= sqrt(2*9.8*24)

= 21.7 m/s

let v2 is the speed both cars after coupling.

apply conservation of moment

m*v1 = (m + m)*v2

==> v2 = v1/2

= 21.7/2

= 10.85 m/s

maximum vartical height reached by the cars,

h2 = v2^2/(2*g)

= 10.85^2/(2*9.8)

= 6.00 m

here h2 < 7 m

it means some one must have pushed the upper car with some initial velocity.

Then only the cars would go in to the lake.

so, The engineer is correct.

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