You have a lightweight spring whose unstretched length is 4.25 cm . You\'re curi

Question

You have a lightweight spring whose unstretched length is 4.25 cm . You're curious to see if you can use this spring to measure charge. First, you attach one end of the spring to the ceiling and hang a 1.12 g mass from it. This stretches the spring to a length of 5.48 cm . You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 5.00 cm .

a) What is the spring constant of the spring? (answer must be in N/m)

b) What is the magnitude of the charge (in nC) on each bead?

(Give your answer in nanocoulombs.)

Explanation / Answer

(A) Fnet = kx - m g = 0

k (0.0548 - 0.0425) = (1.12 x 10^-3) (9.8)

k = 0.89 N/m .......Ans

(b) Fnet = Fe - kx = 0

Fnet = (k q^2 / r^2 ) - k x = 0

(9 x 10^9) (q^2) / (0.05^2) = (0.89) (0.05 - 0.0425)

3.6 x 10^12 q^2 = 6.675 x 10^-3

q = 4.31 x 10^-8 C Or 43.1 x 10^-9 C

q = 43.1 nC .......Ans

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