What path does a balloon on a string follow when a car turns at constant speed?

[deep838]

Hi everyone, I was just wondering about this...

If I tie a balloon outside a car, using a moderately long string, and the car heads for a left turn on the road with constant speed, then while turning, what would be the path followed by the balloon?

I was thinking that maybe the balloon would tend to go in a circular path because of the pseudo force acting perpendicular to its initial direction, but some disagree... Any suggestions?

 

[mfb]

If the car goes in a circle and we do not have wind, the balloon will always go in a circle, too, this just follows from symmetry. The interesting question is the radius of the circle. That depends on the weight of the balloon, air resistance, speed of the car and so on.

 

[deep838]

If the car goes in a circle and we do not have wind, the balloon will always go in a circle, too, this just follows from symmetry. The interesting question is the radius of the circle. That depends on the weight of the balloon, air resistance, speed of the car and so on.

What if the car doesn't go in a circular track, just makes a turn with some radius for some short time interval? Will the balloon still trace a circular path?

 

[mfb]

Probably not, but it will depend on details of the setup.

 

[deep838]

Probably not, but it will depend on details of the setup.

Is there something wrong with the perpendicular force? If that is correct, shouldn't the balloon always try to move in a circle? I am sorry, I am a little biased with this problem, but isn't a force perpendicular to the motion the only requirement of a circular motion? I am not saying that the balloon will make a complete circle, that will depend on the setup, but it should 'want' to go in circles.

 

[rcgldr]

If the car goes in a circle and we do not have wind, the balloon will always go in a circle, too, this just follows from symmetry. The interesting question is the radius of the circle. That depends on the weight of the balloon, air resistance, speed of the car and so on.

Assume that the balloon only has air (not helium) inside of it, and if the string is long enough, the balloon's radius should be smaller. I'm wondering about the case where the string length is the same or longer than the radius of the circle that the car turns, will the balloon eventually stop moving (other than rotating)?

Seem this could be tested with a radio control car and a small balloon.

 

[256bits]

Is there something wrong with the perpendicular force? If that is correct, shouldn't the balloon always try to move in a circle? I am sorry, I am a little biased with this problem, but isn't a force perpendicular to the motion the only requirement of a circular motion? I am not saying that the balloon will make a complete circle, that will depend on the setup, but it should 'want' to go in circles.

A CONSTANT perpendicular force would result in a circular motion for the balloon.

Your thought experiment all depends upon how you describe the "turn" the car is going to make.
With the car itravelling in a straight line, the balloon will be directly behind along the same path.

If the straight line motion of the car is described as a tangent to a circle that the car turns onto, then the radial force, initially zero at the beginning of the turn, will increase to a maximum at which time the balloon will be traveling in a circle of lessor radius than the car. From the start of the turn to the circular motion, the trajectory of the balloon is some kind of spiral.

If the car turn is described as abrupt change in direction of the car so that it begins traveling in a particular circle ( different centre than that above ), such that the balloon's straight line motion becomes a tangent to a circle, then the radial force on the ballloon would be constant.

You could look at it from the opposite scenario where the car and balloon are already traveling in their respective circles. the car could move out into straight line motion tangent to its circle. the balloon would take a spiral path outwards from its circle to eventually follow the car's path.
Or, the car could move out of its cicle, on a straight line trajectory tangent to the balloon's position on its circle so that the balloon immedialely follows the same straight line path as the car.

I guess if you had the wherewithal you could determine the spiral path of the balloon.

 

[deep838]

A CONSTANT perpendicular force would result in a circular motion for the balloon.

Yes I am aware of that...

If the car turn is described as abrupt change in direction of the car so that it begins traveling in a particular circle ( different centre than that above ), such that the balloon's straight line motion becomes a tangent to a circle, then the radial force on the ballloon would be constant.

This is the case I had in mind.

I have to admit, I really didn't think that there could be so many different situations to this same problem, but now that you explained them, I have a much broader view of this. Thanks a lot 256bits!

Assume that the balloon only has air (not helium) inside of it, and if the string is long enough, the balloon's radius should be smaller. I'm wondering about the case where the string length is the same or longer than the radius of the circle that the car turns, will the balloon eventually stop moving (other than rotating)?

Seem this could be tested with a radio control car and a small balloon.

Unfortunately, neither do I have a remote control car nor an actual car :P I can't do it, but if anyone is interested, this can surely be done. If anyone does test this, please let us know in this thread!

 

[rcgldr]

neither do I have a remote control car nor an actual car :P I can't do it, but if anyone is interested, this can surely be done. If anyone does test this, please let us know in this thread!

What about a bicycle towing a balloon on along string?

 

[deep838]

possible! very much! not me, but friends! but are you suggesting that I should use an ordinary balloon instead of a He one?

 

[rcgldr]

possible! very much! not me, but friends! but are you suggesting that I should use an ordinary balloon instead of a He one?

You could test both, but one issue with ordinary is it would get dragged on the ground and could pop.

 

[256bits]

possible! very much! not me, but friends! but are you suggesting that I should use an ordinary balloon instead of a He one?

It doesn't have to be a car and balloon to experiment with the principles.

Since it is summer, why not experiment at this while at the same time having some fun. If you have a boat and some water skis, that is perfect

In the winter, there is ice and pulling around your little nephew or niece on a rope gives both of you bonding time, and a means to experiment at the same time.

 

[256bits]

I have to admit, I really didn't think that there could be so many different situations to this same problem, but now that you explained them, I have a much broader view of this. Thanks a lot 256bits!

The scenario I described would be that for drag in a viscous fluid and pulling a light object.

But wait, there is more.( as mfb alluded to )

Could you consider that the mass of the object and drag on it are such that with the car turning, rather than a spiral trajectory of the object, oscillations are set up in its movement. Rather than the object following a circular orbit, it would move in and out from a mean radius.

The car could make a succession of left and right turns. The object could follow a sinuosoidal (?) path. If the left and right turns of the car are done correctly the value of the objects's sideways motion could be increasingly amplified.

Could you relate all this to spinning a ball on a string attached to the end of a stick where the radius of the ball circle is LARGER than the stick radius?

So, as mfb said, it all depends!

 

[deep838]

Could you consider that the mass of the object and drag on it are such that with the car turning, rather than a spiral trajectory of the object, oscillations are set up in its movement. Rather than the object following a circular orbit, it would move in and out from a mean radius.

As a matter of fact, it did come to my mind when I thought of this experiment. Although it seemed interesting, I wasn't sure of it and that's why I didn't mention it earlier.

The car could make a succession of left and right turns. The object could follow a sinuosoidal (?) path. If the left and right turns of the car are done correctly the value of the objects's sideways motion could be increasingly amplified.

Yes that can be, but its really a complicated situation. I wouldn't want to think about this before the getting a concrete solution of the simple case of the car turning left!

 

[deep838]

Could you relate all this to spinning a ball on a string attached to the end of a stick where the radius of the ball circle is LARGER than the stick radius?

So, as mfb said, it all depends!

Seems similar! the only difference is that there the ball would be down, here the He balloon is up!

Also, here the air plays an important role, something which I didn't want to consider, but I guess I was being stupid about that.

 

[Chestermiller]

Seems similar! the only difference is that there the ball would be down, here the He balloon is up!

Also, here the air plays an important role, something which I didn't want to consider, but I guess I was being stupid about that.

That's right. In fact, air resistance is going to dominate. Actually, the behavior will be approximately the same (under practical conditions) as if the balloon had no mass, in which case centripetal force will be negligible. The only significant forces to consider are the tension on the cord, the air drag force on the balloon, and maybe, to a smaller extent, gravity.

 

[deep838]

Ok. I understand. And then the balloon would start to oscillate in an awkward manner, just like 256bits said.