Question

An unstrained horizontal spring has a length of 0.40 m and a spring constant of 340 N/m. Two small charged objects are attached to this spring, one at each end. The charges on the objects have equal magnitudes. Because of these charges, the spring stretches by 0.033 m relative to its unstrained length. Determine (a) the possible algebraic signs and (b) the magnitude of the charges.

Answer 1

Answer:

(a) Both the charges are positive or negative.

(b) Teh value of each charge is 1.53 x 10^-5 C.

Explanation:

Spring constant, K = 340 N/m

Natural length, L = 0.4 m

stretch, y = 0.033 m

(a) Let the charge on each sphere is q and they repel each other so the nature of charge of either sphere may be both positive or both negative.  

(b) The electrostatic force is balanced by the spring force.

$\frac{kq^2}{(L + y)^2}=Ky\\\\\\\frac{9\times 10^9 q^2}{(0.4 +0.033)^2} = 340\times0.033\\\\q= 1.53\times 10^{-5} C$