Where Am I Going Wrong in Solving Repulsive Charges Problem?

[Dr. S]

Homework Statement

Two 3.0g spheres on 1.0m-long threads repel each other after being equally charged, as shown in the figure.

Homework Equations

F = k*q₁*q₂/r²

The Attempt at a Solution

sin 70° = T_y/T
T = (m*g)/sin 70°
T = 0.003*9.81/sin 70°
T = 0.03132 N

T_x = T*cos 70°
T_x = (0.03132)*cos 70°
T_x = 0.01071 N

Since both objects experience this force, the force is doubled at 0.02142 N.

1/2*r = sin 20°
r = 0.6840 m

T_2x = k*q²/r²
q = (T_2x*r²/k)^1/2
q = [(0.02142)(0.6840)²/(8.99*10⁹)]^1/2
q = 1056 nC = 1.056* 10^-6 C

Where am I going wrong?

 

[PeterO]

Homework Statement

Two 3.0g spheres on 1.0m-long threads repel each other after being equally charged, as shown in the figure.

Homework Equations

F = k*q₁*q₂/r²

The Attempt at a Solution

sin 70° = T_y/T
T = (m*g)/sin 70°
T = 0.003*9.81/sin 70°
T = 0.03132 N

T_x = T*cos 70°
T_x = (0.03132)*cos 70°
T_x = 0.01071 N

Since both objects experience this force, the force is doubled at 0.02142 N.

1/2*r = sin 20°
r = 0.6840 m

T_2x = k*q²/r²
q = (T_2x*r²/k)^1/2
q = [(0.02142)(0.6840)²/(8.99*10⁹)]^1/2
q = 1056 nC = 1.056* 10^-6 C

Where am I going wrong?

I suggest that the line in red is where you went wrong.

during a "tug-of-war", when two teams pull on each end of a sturdy rope, each team pulls with the same force [Newton's third law will show why the forces are equal] but the tension in the rope is just that same value. ie. if each team pulls with 10 000 N, the tension in the rope is 10 000 N [not 20 000 N]

 

[BruceW]

I agree

 

[Dr. S]

sin 70° = T_y/T
T = (m*g)/sin 70°
T = 0.003*9.81/sin 70°
T = 0.03132 N

T_x = T*cos 70°
T_x = (0.03132)*cos 70°
T_x = 0.01071 N

1/2*r = sin 20°
r = 0.6840 m

T_x = k*q²/r²
q = (T_x*r²/k)^1/2
q = [(0.01071)(0.6840)²/(8.99*10⁹)]^1/2
q = 747 nC = 7.47* 10^-7 C

How about now?

 

[BruceW]

looks good to me.

 

[Dr. S]

Got it, thanks guys. :)

(747 nC is correct).