Chapter 22, Problem 32AP

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

# A small sphere of charge q1 = 0.800 μC hangs from the end of a spring as in Figure P22.32a. When another small sphere of charge q2 = −0.600 μC is held beneath the first sphere as in Figure P22.32b, the spring stretches by d = 3.50 cm from its original length and reaches a new equilibrium position with a separation between the charges of r = 5.00 cm. What is the force constant of the spring?Figure P22.32

To determine

The force constant of the spring.

Explanation

Charge on a small sphere is 0.800Â Î¼C, charge on the sphere beneath the first sphere âˆ’0.600Â Î¼C, displacement of spring from its original position 3.50Â cm and separation between the two charges 5.00â€‰cm.

Write the expression for the expression for the spring force according to Hookeâ€™s law

â€‚Â Fs=âˆ’kd Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (1)

Here, Fs is the spring force, k is the spring constant and d is the displacement of the spring

Write the expression for the electric force according to Coulombâ€™s law

â€‚Â F=keq1q2r2

Here, F is the force due to electric field, ke is the Coulombâ€™s constant, q1 is the charge on the first particle, q2 is the charge on the second particle and r is the separation between the two charges.

Substituting 8.99Ã—109Nm2/C2 for ke, 0.8Â Î¼C for q1, âˆ’0.6Â Î¼C for q2 and 5Â cm for r to get F in the above equation,

F=(8

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