You have a lightweight spring whose unstretched length is 4.0 cm. First, you att

Question

You have a lightweight spring whose unstretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 4.9 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 4.7 cm .

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

I got 49 nC, but it turned out to be wrong.

Explanation / Answer

Unstretched length = 4 cm

Stretched length = 4.9 cm

Extension = 0.9 cm = 0.009 m = 9* 10-3 m

Mass = 1 g = 10-3 Kg

Force = mass * g = 9.8 * 10-3 N

Spring constant, k = Force / extension = (9.8*10-3) / (9 * 10-3) = 9.8/9 N/m

After charging

Let the charge on beads be x nC each

On charging, new length = 4.7 cm =4.7 * 10-2 m

Extension = 4.7 - 4 = 0.7 cm = 0.7* 10-2 m

Force due to the charges = k q2 / r2 = (9*109 * x2 * 10-18) / (4.7 * 10 -2)2 = (9 x2 * 10-5) / 22.09 N

Force balanced by spring = -k * extension = - (9.8/9) * (0.7*10-2) N

So the force due to charge and force due to spring balance each other, therefore they are equal in magnitude

=> 9 x2 * 10-5 / 22.09 =(9.8/9) * (0.7*10-2)

=> x = 43.253 nC

Therefore magnitude of charge is 43.253 nC

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