Charged particle suspended from elastic cord

AI Thread Summary
To find the extension of the elastic cord when the charged particle is in equilibrium, a free body diagram is essential. The forces acting on the particle include its weight (mg) acting downward, the restoring force from the elastic cord (kx) acting upward, and the electric force (Fe) also acting upward. At equilibrium, these forces balance, leading to the equation Fe + kx = mg. By substituting the known values into this equation, the extension (x) of the cord can be calculated. This approach effectively determines the equilibrium condition for the charged particle.
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Homework Statement



A charged particle with mass m = 200g and charge q = 25 µC is suspended from an elastic cord with force constant K = 5 N/m in a vertically upward electric field E of magnitude 3.7 x 10^5 N/C. What is extension of the cord when the particle is in equilibrium?

Homework Equations





The Attempt at a Solution

 
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Hi

first draw a free body diagram. there are three forces acting on the body. mg downwards , the force of restoration due to the elastic cord , according to Hook's law is
kx upward and the force due to electric field F_e upward. when in equilibrium, they balance.

F_e+kx = mg

solve for x, the extension.
 

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