A spring with an unstrained length of 0.074 m and a spring constantof 2.4 N/m ha

Question

A spring with an unstrained length of 0.074 m and a spring constantof 2.4 N/m hangs vertically downward from the ceiling. A uniformelectric field directed vertically upward fills the region containgthe spring. A sphere with a mass of 5.1 x 10^-3 kg and a net chargeof +6.6 microC is attached to the lower end of the spring. Thespring in released slowly, until it reaches equilibrium. Theequilibrium length of the spring is 0.059 m. What is the magnitudeof the external electric field?

I am having trouble with this problem. Any help would be greatlyappreciated.

Explanation / Answer

Unstrained length L = 0.074 m

Spring constant k = 2.4 N / m

Mass of sphere m = 5.1 * 10 ^ -3 kg

Charge q = 6.6 * 10 ^ 6 C

Equilibrium length L ‘ = 0.059 m

Compression x = L – L ‘ = 0.015 m

At equilibrium , net force F = 0

                          Eq –Kx –mg = 0

                             Eq = mg + Kx

                                         

From this electi c field E = ( mg + Kx ) / q

                                        = 0.08598 / q

                                        = 13027.27 N / C

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