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

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SUMMARY

The discussion focuses on calculating the spring constant of two identical springs connected to charged spheres. When uncharged, the spheres are spaced 0.05m apart, but with a charge of +1.60 µC on each sphere, the spacing doubles, leading to spring compression. The relevant equations are F = -kx for the spring force and F = k((q1)(q2))/r² for the electrostatic force. By equating these forces and solving for the spring constant, k_spring, one can determine the spring constant based on the amount of compression.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Knowledge of Coulomb's Law (F = k((q1)(q2))/r²)
  • Familiarity with electrostatic charge concepts
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the spring constant using specific values for compression and charge.
  • Explore the relationship between electrostatic force and spring force in detail.
  • Investigate the effects of varying charge on spring compression.
  • Learn about energy conservation in systems involving springs and charged objects.
USEFUL FOR

Physics students, educators, and anyone studying mechanics and electrostatics, particularly in the context of spring systems and charged particles.

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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