A Moving Train Gathers No Coins

Classical Mechanics Level 1

On a moving train, a passenger who is seated facing the front, tosses a coin up in the air. Given that the coin falls into the lap of the person sitting behind this person, what can we say about the motion of the train?

Note:

All the people are facing the front of the train.
All the windows/doors are shut.

It is accelerating It is moving along a circular track It is slowing down It is moving at uniform velocity

8 solutions

Ashutosh Pandey
Jun 3, 2014

As the coin is tossed the coin has the same initial velocity parallel to the train velocity but as the train accelerate and so the person but not the coin with respect to the person, the person is displaced more than the coin and hence the coin falls behind him.

the coin tossed is not connected to the train,. And air flow is not enough to drag the coin with it. So the coin drags behind as the train accelerates.............. I think soo.......... If not pls correct me..............

Ajay SV - 6 years, 12 months ago

I agree with Ashutosh Pandey answer.

Lackhee Meena - 6 years, 12 months ago

AS the train is moving with the velocity V also the Body of the passenger is in the motion .As the Coin is tossed up it's in motion upwards but not forward as compared to the body. meanwhile the coin goes up but the body moves along with the train Body of the passenger got displaced. this is the displacement of the Bodies not the coin, Coin tends to returne to the positionm from where it was being tossed up...! that's it

Munish Sharma - 7 years ago

saurabh gupta I totally agree with u

nikunj gada - 7 years ago

This is wrong. The coin is tossed up within the frame of reference of the train. If the coin went 'back' into the lap of the person behind, it means that the person tossing it tossed it up and back slightly. Its all about relativity. Imagine jumping up on an aeroplane that is accelerating to top speed just after takeoff. Do you suddenly land half way down the fuselage ?

Simon Cochrane - 4 years, 4 months ago

Of course you would! Why would it be compulsory to stay seated and with the seatbelts locked during takeoff and during the first part of the actual flight, when the airplane is still accelerating, otherwise? Would it be just to make the passengers uncomfortable? It is for security reasons! If you'd really try what you claim in your comment above you would cause severe injuries to your (and maybe other people) body, in the best case!

To answer to you and others below, who say that the air inside the train moves together with it, that is absolutely true, but it will move at the same speed of the train only when the train is in uniform motion , as to say that it moves with constant speed. Remember that air is a compressible fluid, and, not being attached to the train body, when the train accelerates, in the air inside it a series of pressure waves (caused by the newly formed air density gradient ) will generate, starting from the back and moving forward, then bouncing at the front of the train and going back again, etc. If it can help you to visualize this process, imagine that, at the very beginning of the acceleration, and for a small time, almost all of the air in the train will be "stuck" or "pressed" against the bottom wall (like people being pressed back on their seats). But air is not a solid body, it is a gas, and so it will expand (move) towards zones with lower pressure (the front of the train), which is the same as saying that it will try to reach again a point of equilibrium (minimum potential energy), as it was the case before the acceleration.

Michele Polli - 1 year, 10 months ago

This is practically wrong as the whole atmosphere inside the train accelerates as the train accelerates practically

Saurabh Gupta - 7 years ago

nothing is wrong in the answer

Anuj Shikarkhane - 7 years ago

You are wrong! Air is a compressible fluid ! The train is filled with air, not water or concrete!

Michele Polli - 1 year, 10 months ago

Write a comment or ask a question..In my opinion, the coin tossed person is at rest but not the tossed coin. So, when the coin is tossed it is in motion but the person is at rest and also train is moving towards, so I think it is moving with average velocity.

Aman Baranwal - 6 years, 11 months ago

I agree with Saurabh Gupta. The whole atmosphere inside the train moves with the train assuming that they are in an enclosed car of the train, or else, if the air around the passengers moves in different velocity or direction, the passengers will feel the air blowing on them. If the coin is tossed vertically by the person whose body is moving with the train, the coin will also have an initial horizontal velocity the same as the body of the person who tossed it and will be carried by the air inside that moves or accelerate with the train, hence it will theoretically fall on the lap of the same person who tossed it. Unless the coin is tossed slightly backwards towards the person at the back.

Emmanuel Jao - 7 years ago

If the train was moving with a uniform velocity that is the velocity was unchanged then the coin would definitely fall on the lap of person who tossed it. But since the train is speeding up the person speeds up as he is on it but the coin is in the air. It will just go up and come down but since the train has moved faster than it was it will fall on the lap of the person behind. But mind you the train would have to accelerate by a very large amount for that.

skaid dkhu - 7 years ago

The coin will be floating in the air once it is tossed. When the train accelerates, the air that carries the coin inside the car will also accelerate. hence the coin will follow the tosser.

Emmanuel Jao - 7 years ago

@Emmanuel Jao – That's smart! Actually I think this problem doesn't consider relative motion. Hence the mistake

skaid dkhu - 7 years ago

@Skaid Dkhu – But remember relative motion works only if your velocity is constant but the train is accelerating.

skaid dkhu - 7 years ago

@Skaid Dkhu – the best solution according to me is to experiment it.

Ansh Bhatt - 7 years ago

@Skaid Dkhu – The air that carries the floating coin is contained in the car of the train. Think of it as a fluid in an enclosed container. The fluid inside the container will always have relative motion with its container; and so with any object that floats in that fluid, they will move together as one.

Emmanuel Jao - 7 years ago

@Emmanuel Jao – Not at all if the fluid you are considering (which is AIR in this case) is compressible . BTW, people won't "feel a breeze" on their faces because of air pressure waves, unless the acceleration is huge (just search for a random video on Youtube about the training of jet pilots, when they are exposed to something like $6$ or $7$ $g$ 's of acceleration in the forward direction, and see by yourself if their faces do or don't deform because of pressure waves), but nonetheless the coin won't be "stuck" to the air that surrounds it, but will move through it like a knife through butter.

Michele Polli - 1 year, 10 months ago

Not sure if that's the correct answer, if the train is accelerating while the coin is tossed in the air, the gas particles inside the train will inevitably move to the back, if that is the case then the train accelerate at a very rapid rate, the same goes for the deceleration of the train, but it would make the coin fall on the lap of the person behind the person who tossed it.

Johnsy Omniscient - 7 years ago

I forgot to mention, if the gas particles inside the train move to the back, the coin must move forward, that is, to the person in front of the person who threw the coin.

This is proven to be true just like a bottle of water is placed sideways and the gas pocket situated above moves to the front as the bottle is also moved to the front.

Johnsy Omniscient - 7 years ago

from the frame of observer on the ground, the coin will appear to do the projectile motion since it has both parallel and perpendicular components of velocity, but, from passenger's(in train), it follows only vetical path, therefore option 2nd and 3rd are most appropriate.....

Genious Shaitan - 6 years, 12 months ago

this is not possible. the coin will fall in the lap of the same person who tossed it.

Ansh Bhatt - 7 years ago

I totally agree with you

Siddhant Chaudhari - 7 years ago

Dang Anh Tu
Jun 3, 2014

I think also we can put an axis here. The origin of this axis is where the coin begun to be tossed, so the coin moved upward (the positive way of the y-axis). So the coin will fall behind the passenger only when the new y-axis will move forward, like the way the train is accelerating (moving forward), so I choose this answer!

Its inertia is same as the initial velocity. As the train accelerates , the velocity of the coin is slower than the train.

Lee Yee Terk - 7 years ago

We need to concider axes because when coin moved upward, it’s velocity depends on passanger’s x-axis component of his velocity (it’s zero at y-axis) and also velocity of passenger’s flipping the coin velocity. Their sum is coin’s velocity so in this case coin’s velocity lower than passenger’s x-axis velocity. This situation leads to coin moving forward slower(slower velocity than train/passenger) than the passenger so the train. Because of that coin left behind of the passenger.

Meltem yurttaş - 1 year, 6 months ago

Subham Gupta
Jun 9, 2014

When the coin is tossed, it has the same velocity as the man who tossed it in the same direction as the moving train. Thus if the train is accelerating its speed is increasing in the same direction and hence the person behind now comes at a position the man who tossed coin would have been if the train would have been moving with a constant velocity.

Ishan Dixit
Jun 8, 2014

As the train is accelarating the passenger who is seated have same accelaration as the train but the coin which is tossed in the air is not connected to the train and has the same velocity all time but train accelarates and hence coin falls on his lap.

Ravi Singh
Jun 4, 2014

when the coin was tossed up it has the same horizontal velocity as that of train ,Since the coin fall on the person sitting behind that means the person who throws the coin has greater displacement than the coin with respect to earth.The loss in the relative velocity of coin w.r.t train is due to the increase in the velocity of the train.

The reason for increase in velocity of train is acceleration, so the answer is train started accelerating.

Niya Monae
Jun 20, 2014

It wasn't that hard to figure out. When solving this problem, I closed my eyes and imagined myself sitting in a front row of a train. If I tossed a coin in the air, and the train is accelerating, the coin would fall behind me. The same happens when I'm on a rollercoaster. If a rollercoaster accelerates, the force causes me to lean back.

I knew that if the train was slowing down, or coming to a slow stop, I would lean forward. Somehow the same as on a bus.

Moderator note:

Yes, but why is it so?

Hardik Nanavati
Jun 4, 2014

wont the position of passenger affect answer???? the person facing the the direction of motion and the person facing opposite side would have different answers...., this struck me after looking at the picture attached to the questions, as even i assumed that the person faces the direction of motion while answering it. please do enlighten me on this.

That is true. If a passenger was sitting opposite the direction of motion, the answer would be equal and opposite, that is, the train is slowing down. This question assumes that the passenger is facing the direction of motion. The question should be amended to reflect this.

Arun Nagpal - 7 years ago

Thanks for bringing this into our attention. We have added the clarification.

Brilliant Mathematics Staff - 6 years, 1 month ago

Mihirpushp Bisht
Jun 4, 2014

accelerated as the moment the coin was tossed it gained a certain velocity of train at that moment. but when the coin fell, the train was having more velocity.

What will happen if the train run at uniform velocity (high)? When the coin threw up it must get the initial motion of the train but when the up speed will be zero and start to fall down thn the coin shouldn't have the initial motion of train. The train is moving forward and the coin is falling down straight. In that case, will not the coin fall on lap of the passenger behind the toaster?

Suman Dhar - 7 years ago

A Moving Train Gathers No Coins

8 solutions

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