Question

Two charged objects are connected to a spring with force constant k = 500 N/m and unstretched length L_0 = 50 cm. The magnitude of each charge is the same. The charge on the left is fixed to the wall, but the charge on the right is free to move on the frictionless surface (stretching or compressing the spring) until it reaches equilibrium. If the objects are 1.0 m at equilibrium, what is the magnitude of each charge? 167 mu C If the objects have 30-mu C opposite charges, what is their separation at equilibrium? 0.259 m, 0.397 m If the objects have 30-mu C like charges, what is their separation at equilibrium? 0.553 m

Answer 1

40) The force on the second are

kx - kq^2/R^2 = 0 ;

500 * (1-.5) = k q^2/R2

q = sqrt (250/9*10⁹)

q = 167 uC

41 ) writing the similar equation

K ( .5 - R ) = k Q^2/R^2

250 R^2 - 500 R^3 = 9*10⁹ * 9*10^-10

250 R^2 - 500 R^3 = 8.1

Hence R = .259 m and 0.397 m

42 ) The similar equation just changes the sign

K ( R - .5) = k Q^2/R^2

250 R^2 + 500 R^3 = 9*10⁹ * 9*10^-10

R = 0.553 m