Rainbow Train

An engine pulls three carriages of equal masses. Consecutive carriages are connected with a coupling.

If the train is accelerating forward, then in which coupling is the tension greatest?

Indigo Green Orange Tension is equal in all three couplings

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Tapas Mazumdar
Sep 26, 2016

Consider the net external force provided by the engine be F F and the kinetic friction between each of the carriages and the rail-track be f f .

Now, tension in the orange coupling (neglecting mass of coupling) = F f = F - f

The first carriage is moving forward with net external force F f F-f and the kinetic friction between second carriage and rail-tack is f f .

So, tension in green coupling (neglecting mass of coupling) = ( F f ) f = F 2 f = (F - f) - f = F -2f

Similarly tension in indigo coupling = F 3 f = F - 3f

Hence tension in the n t h n^{th} coupling = F n f = F - nf .

From, here we conclude that the tension in the coupling furthest from the engine keeps on decreasing as we increase the number of carriages.

Therefore, tension remains maximum at the coupling nearest to the engine, i.e. , the coupling with the color Orange \boxed{\text{Orange}} .

Luke Brace
Oct 23, 2016

The orange has the mass of all the carts especially when accelerating and desecrating ?? Maybe? I thought this might be the simple answer. Feel free to tell me if I'm wrong

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...