Electric Charges: Newton's Third Law & Tension

[DarylMBCP]

Hi, I hve kind of a problem with this static electric question; There are two SIMILAR ping pong balls coated with aluminium paint and suspended using nylon string. Taking the imaginary line perpendicular to the wall, on which the balls are hanging from, to be the normal (although this is in light), the ball on the right, W, is at an angle 2x from the normal while the other one, Z, is at an angle x from the normal, after both of them were charged.
The question is whther the charge on W is smaller than the charge on Z and the answer is true. However, shouldn't both angles from the normal be equal due to Newton's Third Law; Action = Reaction? Also, does the answer have anything to do with the tension of the string, as I hve read that the greater the angle from the normal, the lesser the tension of the string. I am not rlly sure how to prove this mathematically or using Physics formulas. Any help is greatly appreciated as I'm quite new to this topic. Thanks.

 

[kbaumen]

Hi, I hve kind of a problem with this static electric question; There are two SIMILAR ping pong balls coated with aluminium paint and suspended using nylon string. Taking the imaginary line perpendicular to the wall, on which the balls are hanging from, to be the normal (although this is in light), the ball on the right, W, is at an angle 2x from the normal while the other one, Z, is at an angle x from the normal, after both of them were charged.
The question is whther the charge on W is smaller than the charge on Z and the answer is true. However, shouldn't both angles from the normal be equal due to Newton's Third Law; Action = Reaction? Also, does the answer have anything to do with the tension of the string, as I hve read that the greater the angle from the normal, the lesser the tension of the string. I am not rlly sure how to prove this mathematically or using Physics formulas. Any help is greatly appreciated as I'm quite new to this topic. Thanks.

Could similar imply close-to-equal, although different masses?

 

[tiny-tim]

Hi DarylMBCP!

Won't one ping-pong ball be higher than the other?

 

[DarylMBCP]

Hi guys, thanks for the help. Anw, I'm not rlly sure if tht is wht the question implies but I don't think it rlly matters as the answer key states smething out of the blue; tht the charge on W must be smaller than the charge on Z for the balls to be repelled such that one is higher than the other. Does this mean tht Z exerts a stronger force on W than wht W exerts in Z? Anw, I thought tht regardless of the electric charges of both balls, the net force acting on both should be the same (Newton's third law)?

 

[tiny-tim]

the answer key states … tht the charge on W must be smaller than the charge on Z for the balls to be repelled such that one is higher than the other. Does this mean tht Z exerts a stronger force on W than wht W exerts in Z? Anw, I thought tht regardless of the electric charges of both balls, the net force acting on both should be the same (Newton's third law)?

Yes, Newton's third law does say that …

but the tensions in the supporting strings are different, and the combined tension and electric charge are different, which is what matters.

 

[DarylMBCP]

Hey Tim, thnks for the help. Anw, isn't the tension in the string dependent on the weight of the balls and the net forces acting on them? If so, take the weight of the balls to be equal (as if the balls were of different masses, they would be able to be lifted to different heights) and since the net forces acting on the balls are equal, shouldn't the tensions of the strings be equal?

 

[tiny-tim]

Hey Tim, thnks for the help. Anw, isn't the tension in the string dependent on the weight of the balls and the net forces acting on them? If so, take the weight of the balls to be equal (as if the balls were of different masses, they would be able to be lifted to different heights) and since the net forces acting on the balls are equal, shouldn't the tensions of the strings be equal?

Hey DarylMBCP!

Who is putting this egalitarian nonsense into your head?

Forget democracy … everyone is not equal …

yes, the mass and the string-length are the same, but the charges are different, so there's no symmetry, so why should the tensions be equal?

 

[DarylMBCP]

Sry abt tht, I'm still quite confused. Anw, the charges are different but the resultant force acting on both balls should be the same as we spoke earlier, right? Other than tht, I knw tht the weight and resultant forces shld be the same too, right?

 

[tiny-tim]

Sry abt tht, I'm still quite confused. Anw, the charges are different but the resultant force acting on both balls should be the same as we spoke earlier, right? Other than tht, I knw tht the weight and resultant forces shld be the same too, right?

(just got up :zzz: …)

The resultant force?

The resultant force on each weight will be zero.

If you mean the tension and the electric force combined, then yes they will be the same because they will be equal and opposite to the weight …

but the tension and the electric force combined being equal doesn't make them equal separately.

 

[DarylMBCP]

Ok, I get tht electric force acting on the balls is different, but how is this possible, since the action force acting on one ball should be the same as the reaction force from tht ball onto the first one? Tht's the confusing part.

 

[tiny-tim]

Ok, I get tht electric force acting on the balls is different, but how is this possible, since the action force acting on one ball should be the same as the reaction force from tht ball onto the first one? Tht's the confusing part.

Force is a vector … it has a direction …

the electric forces aren't equal … they're the opposite of equal …

in fact, they're opposite … you can't get any more unequal than that!

draw a vector triangle for each ball (separately) …

they'll both have vertical sides of the same length (for the weight), and sloping bases of the same length (for the electric force), but one will slope down to the left, and the other will slope up to the right, so the third sides (the tensions) will be different lengths, and at different angles.

 

[DarylMBCP]

Omg, I kept thinking tht the electric force arrows would be horizontal lines(dotted lines) instead of pointing away from each other depending on their positions(full-black line). Thanks for pointing tht out, but how did the balls achieve tht position since the electric forces and vertical line for the weight should hve been of the same length on both sides causing the tension to be the same on both sides? How did this change in position occur?

 

[tiny-tim]

… but how did the balls achieve tht position since the electric forces and vertical line for the weight should hve been of the same length on both sides causing the tension to be the same on both sides? How did this change in position occur?

hmm … looking back, I see that I originally asked for clarification as to whether one ball was higher than the other, and then we got side-tracked into a discussion of how that could be …

I rather lost sight of the fact that the question was about the ratio of the charges …

let's see again what the original question said …

There are two SIMILAR ping pong balls coated with aluminium paint and suspended using nylon string. Taking the imaginary line perpendicular to the wall, on which the balls are hanging from, to be the normal (although this is in light), the ball on the right, W, is at an angle 2x from the normal while the other one, Z, is at an angle x from the normal, after both of them were charged.
…
The question is whther the charge on W is smaller than the charge on Z and the answer is true.

ok …

we know that the point halfway between the two balls must be vertically below the point of suspension (because it's the c.o.m.) …

but we are told that the angles are different …

so (using simple geometry) that itself tells us that one ball must be higher than the other, and therefore one string must be shorter than the other.

I therefore assume that it's given that one string is shorter than the other, in which case the reason why the angles are different is pure geometry (plus the c.o.m. having to be below the point of suspension), and has nothing to do with the ratio of the charges: the angles would be the same if the product of the charges is the same (because the product determines the forces, which as you say must be equal and opposite ), no matter what their ratio is.

I can't see your picture yet, which is still rather confusing me , but it looks as if your suspicion is right, and the answer given is wrong, not because the charges can't be different, but because they needn't be different.

 

[DarylMBCP]

Actually, I think I get wht y're saying, but just to check, the only possible reasoning tht one ball could be higher than the other ball, if both balls are identical, is tht the string is shorter on the side with the ball tht is higher, despite their charges, right?

 

[tiny-tim]

Actually, I think I get wht y're saying, but just to check, the only possible reasoning tht one ball could be higher than the other ball, if both balls are identical, is tht the string is shorter on the side with the ball tht is higher, despite their charges, right?

Yes, the only external forces are the weights, and the reaction at the point of suspension …

so if the mass and the string-lengths are the same, then the centre of mass must be below the point of suspension (whatever the internal forces, such as charge and tension, are), and so the balls must be level.

 

[DarylMBCP]

K, thnks for all the help. I get it now.