Spring Constant Due to 2 Charges

[mrlucky0]

Homework Statement

A tiny sphere with a charge of q = +6.1 µC is attached to a spring. Two other tiny charged spheres, each with a charge of -4.0 µC, are placed in the positions shown in the figure, in which b = 3.6 cm. The spring stretches 5.0 cm from its previous equilibrium position toward the two spheres. Calculate the spring constant.

(See attachment)

Homework Equations

Coulomb's law:
F = Kq1q2/r^2

Spring Constant:
F = kx

The Attempt at a Solution

I determine the net force due to to the individual force caused by F1 and F2:

F1 = kq1q2/r^2 * < cos(a), -sin(a) >
F2 = kq1q2/r^2 * < -cos(a), -sin(a) >

Fnet = F1 + F2

Where q1 = 4E-6 C, q2 = 6.1E-6 C, r = .0412 m ( by Pythagorean theorem) , a = 61 degrees

Fnet = < 0, -3.8E-1 >
||Fnet|| = 3.8E-1 N ; This is force due to the two charges pulling down on the spring.

F = kx
Sub in values:

3.8E-1 = k*(.036) ===> k = 11

The spring constant is 11 N/m ?

 

[rootX]

for Fnet = < 0, -3.8E-1 >

are you sure that this is correct?

Edit: because each time I do the calculations I get like > 100 N or about that

 

[learningphysics]

Yeah, I get kq1q2/r^2 for one of the spheres to be 129.48N, then the vertical component is 129.48*sin(61) = 113.2N

Then 2 of them so 2*113.2N = 226.5N

226.5N = kx
226.5N = k(0.05m)

k = 4530N/m ?

 

[mrlucky0]

Yeah, I get kq1q2/r^2 for one of the spheres to be 129.48N, then the vertical component is 129.48*sin(61) = 113.2N

Then 2 of them so 2*113.2N = 226.5N

226.5N = kx
226.5N = k(0.05m)

k = 4530N/m ?

Thanks. You're absolutely right. I was making it more complicated than it was with the vectors which should of gotten me the right answer but I goofed up. The net force pulling the spring down is simply a vector pointing straight down. Here's what I was thinking:

kq1q2/r^2 * [ <cos(a), -sin(a)> + <-cos(a), -sin(a)>]
= kq1q2/r^2 * <0, -2sin(a)>
<0, -226.5 >

Take the magnitude of that vector to find k:

226.5 = k ( 0.05 m ) ==> k = 4530 N/m

Thank you again.

 

[rootX]

hey,
what book you are using?

 

[mrlucky0]

hey,
what book you are using?

College Physics

Giambattista
Richardson
Richardson

 

[rootX]

thanks.