Solve Electric Force II Homework Problem

[Goldenwind]

[SOLVED] Electric Force II

Homework Statement

You have a lightweight spring whose unstretched length is 4.0 cm. You're curious to see if you can use this spring to measure charge. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5.0 cm. You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 4.5 cm.

What is the magnitude of the charge (in nC) on each bead?

Homework Equations

F = -k1 * x
F = k2 * q1q2 / r^2

g = a = -9.81
k1 = Spring constant. Unknown.
k2 = Electrostatic constant = 9*10^9

The Attempt at a Solution

In the first experiment
F = ma = -k1*x
0.001*-9.81 = -k1*(0.05 - 0.04)
Therefore the spring constant k1 = 0.981

Now the second experiment:
F = -k1*x
F = -(0.981)(0.045 - 0.04)
F = -0.004905
This is the force applied on a spring of k1 = 0.981, to stretch it 0.5cm

Similarily, this should also be the force between the two beads:
F = k2*q1q2 / r^2, however q1 = q2 according to the question.
F = k2*(2q) / r^2, solving for q.
Fr^2/(2*k2) = q
(-0.004905)(0.045)^2/(2*9*10^9) = q

q = -0.0000000000000005518125 C
q = -0.0000005518125 nC

This answer is incorrect.
Where is my mistake?

 

[Doc Al]

Similarily, this should also be the force between the two beads:
F = k2*q1q2 / r^2, however q1 = q2 according to the question.

OK.

F = k2*(2q) / r^2, solving for q.

That should be q^2, not 2q.

 

[Goldenwind]

OK.

That should be q^2, not 2q.

I almost feel like I'm wasting your time, as my mistakes seem so trivial..

F = k2*q1q2 / r^2, however q1 = q2 according to the question.
F = k2*(q^2) / r^2, solving for q.
Sqrt((Fr^2)/k2) = q
Sqrt((-0.004905 * 0.045^2)/(9*10^9)) = q
Sqrt(-0.000009932625 / 9000000000) = q
q = -0.000000000000001103625 C
q = -0.000001103625 nC
q = -1.103625 * 10^-6 nC

This answer is also incorrect. While what you pointed out was indeed a mistake I made, there appears to be more >.<;
Reading over it again.

 

[Doc Al]

I almost feel like I'm wasting your time, as my mistakes seem so trivial..

F = k2*q1q2 / r^2, however q1 = q2 according to the question.
F = k2*(q^2) / r^2, solving for q.
Sqrt((Fr^2)/k2) = q
Sqrt((-0.004905 * 0.045^2)/(9*10^9)) = q
Sqrt(-0.000009932625 / 9000000000) = q

This is OK. (But get rid of that minus sign!)

q = -0.000 000 000 000 001 103625 C

Looks like you didn't take the square root.

(Please use scientific notation. All those zeroes are opportunities for error. And hard to read! )

 

[Goldenwind]

This is OK. (But get rid of that minus sign!)

Looks like you didn't take the square root.

(Please use scientific notation. All those zeroes are opportunities for error. And hard to read! )

F = k2*q1q2 / r^2, however q1 = q2 according to the question.
F = k2*(q^2) / r^2, solving for q.
Sqrt((Fr^2)/k2) = q
Sqrt((0.004905 * 0.045^2)/(9*10^9)) = q
Sqrt(9.932625*10^-6 / 9*10^9) = q
q = Sqrt(1.103625*10^15)
q = 3.3220851885525151294968428473179*10^-8 C
q = 33.221 nC

Checking... correct!

Doc Al is saving my education.
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