We have a physics exam tomorrow, and have been presented with a previous exam for practice. One of the assignments have puzzled us quite a bit. Here goes:(adsbygoogle = window.adsbygoogle || []).push({});

Rain in a train wagon

Consider a train wagon whose upper part is a lidless box. The train wagon moves without friction. There is water in the train wagon. In the following the system consisting of the train wagon and the water in it is considered. In 3 different situations (i,iiandiii) decide what happens with each of the three variables speed [itex]v[/itex], momentum [itex]p[/itex] and the kinetic energi [itex]K[/itex].

(i)It's raining vertically, and water is accumulated in the wagon.

(ii)As in (i) with the addition that there's now a hole in the bottom where the water's running out. The amount of water running out of the wagon is equal to the amount of water raining into the wagon.

(iii)The rain stops, but there is still a hole in the bottom of the wagon, where the water's running out.

Answers

Since we've been given the results (the correct answers, no explanations), I'm not interested in that information. Only the explanation.

(i)Result: Momentum is conserved, [itex] p [/itex] is not changed. I guess the system is a closed system. The speed [itex] v [/itex] decreases - because mass [itex] m [/itex] increases. Thus the kinetic energy [itex] K [/itex] drops too, since [itex] K [/itex] is proportional to the square of [itex] v [/itex].

(ii)Result: All three variables, [itex] p, v, K [/itex] drops. It's clear that since the mass is the same, a speed decrease causes the momentum and energy decrease. But why does the speed [itex] v [/itex] drop?

(iii)Result: Here, water is running out, and thus the mass [itex] m [/itex] decreases. This causes a decrease in [itex] p [/itex] and [itex] K[/itex], since the speed [itex] v [/itex] doesn't change. But why does the speed [itex] v[/itex] change in (i) and not in (iii) ?

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# Homework Help: Rain in a train wagon - speed, momentum and KE

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