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        riddles >> general problem-solving / chatting / whatever >> Ping Pong Ball Question
        
(Message started by: Padfoot on Mar 19^th, 2007, 3:02pm)

Title: Ping Pong Ball Question
Post by Padfoot on Mar 19^th, 2007, 3:02pm

Imagine you traviling in a car with a very high roof. If you toss a ping pong ball up in the air and then quickly accelerate, what happons to the ping pong ball?

Title: Re: Ping Pong Ball Question
Post by towr on Mar 19^th, 2007, 3:30pm

If your car is entirely filled with water, it'll move forwards (and of course up, since pingpong balls float).
Normally it would move backwards (noticably relative to the car, but also a bit relative to the ground)

Title: Re: Ping Pong Ball Question
Post by Icarus on Mar 19^th, 2007, 3:45pm

If the ping pong ball was in a vacuum, then it would go straight up relative to the ground. Relative to the car, it would appear to accelerate towards the rear.

Now put air in. Accelerating causes increased pressure in the air in the back of the car and decreased pressure at the front. This pressure difference pushes the ping pong ball forward. But since the ping pong ball is significantly denser than the air, the effect is small. So the ball still moves backwards relative to the car, but slightly forwards relative to the ground.

This is different from what happens to a helium balloon in an accelerating car (or what happens to the ping pong ball in water). In that case, the pressure difference actually pushes the balloon in the direction of travel. I.e., the balloon moves forward with respect to the car when the car accelerates (I've actually observed this, so it isn't just theory).

Title: Re: Ping Pong Ball Question
Post by BNC on Mar 19^th, 2007, 4:26pm

on 03/19/07 at 15:45:34, Icarus wrote:

(I've actually observed this, so it isn't just theory).

What, a ping pong ball in a car full with water?? :o

Title: Re: Ping Pong Ball Question
Post by Padfoot on Mar 19^th, 2007, 5:12pm

Thanks for the explanation.

on 03/19/07 at 15:45:34, Icarus wrote:

This is different from what happens to a helium balloon in an accelerating car (or what happens to the ping pong ball in water). In that case, the pressure difference actually pushes the balloon in the direction of travel. I.e., the balloon moves forward with respect to the car when the car accelerates (I've actually observed this, so it isn't just theory).

That's interesting. I had always thought that it would move back in respect to the car but I guess I learned something new. :)

Title: Re: Ping Pong Ball Question
Post by Icarus on Mar 19^th, 2007, 8:24pm

Actually, when you consider Einstein's Principle of Equivalence, it's obvious. That may sound like something "high-falutin'", but actually the Principle of Equivalence is simple: Acceleration due to gravity is no different than mechanically induced acceleration.

I.e., the acceleration of the car is identical to the situation where the car is standing with its nose up in a higher gravity field. In that static situation, you would expect the balloon to rise just like normal. "Rising" is moving towards the nose of the car.

Title: Re: Ping Pong Ball Question
Post by towr on Mar 20^th, 2007, 1:15am

Then you'd expect the pingpong ball to move backwards, wouldn't you. Because it falls in gravity. Rather than rise like a helium balloon.

Title: Re: Ping Pong Ball Question
Post by rmsgrey on Mar 20^th, 2007, 6:31am

on 03/20/07 at 01:15:18, towr wrote:

Then you'd expect the pingpong ball to move backwards, wouldn't you. Because it falls in gravity. Rather than rise like a helium balloon.

Relative to the car, not to the ground...

If you fix the car as your frame of reference, and treat the acceleration forces as gravitational ones, then the ground appears to be accelerating past the wheels in "free-fall" (as far as the horizontal component goes), so, since the air in the car cushions its "fall" somewhat, the ball isn't "falling" as fast as the ground outside.

Title: Re: Ping Pong Ball Question
Post by Iceman on Mar 20^th, 2007, 8:19am

on 03/19/07 at 15:02:50, Padfoot wrote:

Imagine you traviling in a car with a very high roof. If you toss a ping pong ball up in the air and then quickly accelerate, what happons to the ping pong ball?

First, you have to know, that every action has its reaction. So, what is your action? You toss a ping-pong ball up in the air inside of the car with a very high roof. If the roof is thin, the ball will get stuck right at the beginning of it. But if roof is spacious, then this is what happens: if windows are opened, the flow of air will disturb the straightforward path of the ball. So, the ball will bounce seven times, and then finally land on your head. And if you have thick hair, it will stay on your head. If you are bold, then it will fall in your lap. But if the windows are closed, then the ball will travel no more than a meter, because this particular ball is very light. And since you have said that the roof if very high, we can deduce that the ball will never touch the roof. 8)

Title: Re: Ping Pong Ball Question
Post by Grimbal on Mar 20^th, 2007, 8:29am

If you drive while tossing a ping pong ball in the air and observing the trajectory of the ball carefully while accelerating wildly, you will notice that the ping pong ball is likely to follow the path of the car, namely straight into a tree off the road.

Title: Re: Ping Pong Ball Question
Post by Padfoot on Mar 20^th, 2007, 2:59pm

on 03/20/07 at 08:29:44, Grimbal wrote:

Title: Re: Ping Pong Ball Question
Post by JiNbOtAk on Mar 20^th, 2007, 9:05pm

on 03/20/07 at 08:29:44, Grimbal wrote:

Damn Grimbal, you should stop doing that ! My colleagues thought I was starting to go mad, laughing out loud all of a sudden.. ;D

What if we are to replace the ping pong ball with a beam of light ( with a mirror attached to the roof ) ? Would the behaviour ( in terms of its speed and displacement ) be the same ?

Title: Re: Ping Pong Ball Question
Post by Icarus on Mar 21^st, 2007, 6:15pm

The light, having left its source, is not longer affected by the movement of the car. Assuming that the car was at rest (with respect to the ground) when the light was emitted, then starts accelerating extremely fast while the light travels, the light will continue to travel straight up and down with respect to the ground, but when it returns to its source, the source has moved and is no longer there.

To the observer outside the car, the light travels up and down. To the observer inside the car, the light is "pulled aft" by the acceleration.

Now, apply Einstein's principle of equivalence again to see why gravity affects light!

Title: Re: Ping Pong Ball Question
Post by JiNbOtAk on Mar 21^st, 2007, 8:27pm

on 03/21/07 at 18:15:56, Icarus wrote:

To the observer outside the car, the light travels up and down. To the observer inside the car, the light is "pulled aft" by the acceleration.

Hey, that's weird, I've always thought it would be the other way round, with the observer in the car seeing the light travelling up and down, whereas someone outside would see it slanting..

Title: Re: Ping Pong Ball Question
Post by Grimbal on Mar 22^nd, 2007, 1:46am

The light would move forward relative to the road if the laser emitting the light was moving at the time of the emission.

Title: Re: Ping Pong Ball Question
Post by Icarus on Mar 22^nd, 2007, 3:27pm

Yes. It is the acceleration of the car that produces the affect here. If the car is just traveling at a constant velocity, the velocity of the car adds to the light when it is emitted. So the person inside sees the light move straight up and down, while the person outside sees the light travel sideways along with the car.

But the situation with the accelerating car is different. Because I specified that the car is at rest when the light is emitted, its direction of travel is straight up and down with respect to the ground. The later acceleration of the car does not affect the light - there is nothing pushing the light to the side - so the outside person continues to see the light travel straight up and down. The car moves during the light's trip, though. So to someone inside, it appears that the light bends.