How Do You Calculate the Spring Constant in a Charged Sphere Setup?

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To calculate the spring constant in a charged sphere setup, the force between the spheres can be expressed using Coulomb's law, F = k(q1q2)/r^2, where q1 and q2 are the charges of +1.60 µC each. When the spheres are charged, the distance between them doubles, affecting the spring's compression. The spring's force can be represented as F = -k_spring * x, where x is the compression of the spring. By equating the two force equations, the spring constant can be determined using the known values of charge and distance. Understanding the relationship between the forces allows for the calculation of the spring constant effectively.
allyson6018
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Two spheres are mounted on two different identical horizontal springs and rest on a frictionless table (one spring is connected to the left side of a wall with a sphere attached to the other end & the other sphere is connected to the other spring which is connected to the other wall -- both spheres are facing each other) When the spheres are uncharged, the spacing between them is .05m, and the springs are unstrained. When each sphere has a charge of +1.60 uC, the spacing doubles (springs compress). Assuming that the spheres have a negligible diameter, determine the spring constant of the springs.

Okay so I know F= -kx, F=k [((q1)(q2)) / r^2] but I am not quite sure how to connect the dots...and what would q1 and q2 be? I am confused...

Please HELP!
 
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allyson6018 said:
Okay so I know F= -kx, F=k [((q1)(q2)) / r^2] but I am not quite sure how to connect the dots...and what would q1 and q2 be? I am confused...
The charge on each sphere is given. How much does each spring compress?
 
q1 and q2 are the charges of the spheres, which is +1.60 micro C. r is the distance between the charges, which is double the original spacing between the spheres. Keep in mind that the two k's you have written in the equations above are not the same!

Anyways, you have the force F exerted onto the spheres (from F = (kq1q2)/r^2). Using F = -k_spring x, you can find the spring constant. All you need is x, which is the amount of compression.
 
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