Three charges in a plane- static and current electricity

[name_ask17]

Homework Statement

An equilateral triangle has sides of 0.11 m. Charges of -8.6, +8.0, and +1.5 µC are located at the corners of the triangle. Find the magnitude of the net electrostatic force exerted on the 1.5-µC charge.

Homework Equations

kqQ/d^2

The Attempt at a Solution

first i did kq1q3/d^2 and got F13=9.595
then i did kq2q3/d^2 and got F12=8.9256

then i set up f12x=8.9256cos60 +f13x=9.590 to get Fx=14.05and then F12y=8.9256sin60 + f13y=0 to get Fy=7.73
then i used the pythagaron theorem to get the total force on q3 as 16.0359N, but that was marked incorrect by the online hw.
can you explain to me where I am going wrond please??

 

[gneill]

In what direction does F13 act compared with the x-component of F12?

 

[name_ask17]

they act in opposite directions. but if 1 was negative, then that would still come out as the same answer when i do the pythagaron theorem correct? or no?

 

[gneill]

I don't see any negative values in the sums you provided back in post #1. When you add components, you have to rely on algebraic signs to indicate directions.

 

[name_ask17]

ok so they are both positive, but where am i going wrong? did i miss a step? because my book has a example of this type of problem and it is very similar and i am doing everything it did,please advise

 

[SammyS]

Homework Statement

An equilateral triangle has sides of 0.11 m. Charges of -8.6, +8.0, and +1.5 µC are located at the corners of the triangle. Find the magnitude of the net electrostatic force exerted on the 1.5-µC charge.

Homework Equations

kqQ/d^2
This is not an equation; no equal sign.

The Attempt at a Solution

first i did kq1q3/d^2 and got F13=9.595
then i did kq2q3/d^2 and got F12=8.9256

then i set up f12x=8.9256cos60 +f13x=9.590 to get Fx=14.05and then F12y=8.9256sin60 + f13y=0 to get Fy=7.73
A customary way to write these is:
F_x=(F₁₂)_x+(F₁₃)_x → F_x=(8.9256)cos(60)+9.590
and
F_y=(F₁₂)_y+(F₁₃)_y → F_y=(8.9256)sin(60)+0
then i used the Pythagorean theorem to get the total force on q3 as 16.0359N, but that was marked incorrect by the online hw.
can you explain to me where I am going wrong please??

Comments in red above.

Does charge 2 attract or repel charge 1 ?
Does charge 3 attract or repel charge 1 ?

Writing "f12x=8.9256cos60 +f13x=9.590", etc. means something completely different from what you intend.

 

[name_ask17]

charge 2 attracts charge 1; charge 3 also attracts charge 1. so what do i do from here?

 

[gneill]

charge 2 attracts charge 1; charge 3 also attracts charge 1. so what do i do from here?

Well, you sum up the components making sure to take into account their signs (directions). If two forces are acting in opposite directions, their sum should be smaller than either one individually.

 

[name_ask17]

OH! thanks. i was not taking the (-) into account; thanks both(:

 

[SammyS]

From your equations & results, it looks to me like charge 1 = +1.5 µC, charge 2 = +8 µC, and charge 3 = ‒8.6 µC.

So charge 2 repels charge 1 and charge 2 attracts charge 1. .. and you're looking for the force on charge 1.

But looking back on them all, perhaps they're inconsistent or at the very least, confusing.

At any rate, as regards the two forces your trying to add, one is attraction, one is repulsion.