Two initially uncharged identical metal spheres are connected by an insulating spring (unstretched length 0.75 m,spring constant k=35.0 N/m).Charge +2q is placed on the first sphere and -q on the second sphere,causing the spring to contract to a length of 0.54 m.Recall that the force exerted by a spring is k$\Delta$x,where $\Delta$x is the change in the spring's length from its unstretched/uncompressed length.Determine the charge q. A)1.19 * 10^-10 C B)1.09 * 10^-5 C C)2.06 * 10^-5 C D)1.75 * 10^-5 C E)3.62 * 10^-5 C

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Quizplus · Accepted Answer

The force exerted by the spring is equal to the electrostatic force between the two spheres. The spring's force can be calculated using Hooke's law, $F = k \Delta x$, where $\Delta x = 0.75m - 0.54m = 0.21m$. Thus, $F = 35.0 N/m \times 0.21m = 7.35N$. The electrostatic force is given by Coulomb's law, $F = \frac{k_e |q_1 q_2|}{r^2}$, where $k_e = 8.987 \times 10^9 Nm^2/C^2$, $q_1 = 2q$, $q_2 = -q$, and $r = 0.54m$. Solving for $q$ gives $q \approx 1.09 \times 10^{-5} C$.

Two Initially Uncharged Identical Metal Spheres Are Connected by an Insulating