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Q & A: Jumping up and down on a train going 60 mph?

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Most recent answer: 08/22/2013
Q:
if i were on top of a train at 60mph and drew a circle around myself and jumped in the air would i land back in the circle
- steve sanderson
Carlisle
A:
On top of the train? Come on, you've got to be kidding.  You can't even stand up in a 60 mph wind.  You would be blown away.   Now if you were inside the train going at a constant velocity the answer is yes.  Both you and the train are going 60 mph and there is no wind or any other force to move you relative to the train.   If the train is speeding up, braking, or making a turn the answer is again no.   There are acceleration forces on the train but not on you when you are in the air.  So effectively the train moves out from under you.

LeeH

(published on 07/16/2012)

Follow-Up #1: How do objects move in accelerating frames?

Q:
What if your were a fly in a train going 60mph? If the train decelerated would the fly move forward or stay in place?
- Lisa (age 34)
Jessup, md usa
A:

Hey Lisa,

Interesting question. In general, in a decelerating frame objects act as if there's a force forwards on them. For this reason, when you slam on the brakes in your car, you are thrown forward and bang your head on the dashboard.

However, it's important to remember that everything in this frame gets thrown forward also. For example, flies and air molecules and helium balloons are thrown forward also. So what happens to a helium balloon in a decelerating train?

While you are thrown forwards, a helium balloon is actually thrown backwards when you slam on the brakes! This happens (even though there is a forward force on the balloon from the decelerating frame!) because the air around the balloon is heavier than the balloon itself, so when the air is thrown forward, it pushes the balloon out of the way (i.e. backwards). You can find cool videos of this on Youtube.

Aside: here's a slick way to prove what I just argued. Einstein's theory of equivalence says that a reference frame with acceleration can be modeled exactly by an inertial frame with a force of gravity in the opposite direction. We know that helium balloons move in the opposite direction as gravity (since they are lighter than air). So, if we slam on the brakes (accelerate backwards), we feel an "effective" gravitational pull towards the front, and so the helium balloon moves against this towards the back. Awesome!

So, what happens to a fly? Well, a fly is a lot heavier than an air molecule, so it flies forward just like a human.

Hope that long answer satisfies your curiosity!

David Schmid


(published on 08/22/2013)

Follow-up on this answer.