A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the initial charge on the capacitor is:
A) 0.15 C
B) 6.67 C
C) 0.025 C
D) 40 C
E) 35 C

Question

Quizplus · Accepted Answer

The electrical analog for a block-spring system is a capacitor-resistor system, where the charge on the capacitor (q) corresponds to the displacement of the block (x), and the capacitor's capacitance (C) corresponds to the spring constant (k).

We can use the equation for the potential energy stored in a spring: 
PE = 1/2kx^2

And the equation for the energy stored in a capacitor: 
PE = 1/2q^2/C

Equating these two expressions, we get: 
1/2kx^2 = 1/2q^2/C

Plugging in the given values, we get: 
1/2(35 N/m)(0.25 m)^2 = 1/2q^2/C

Solving for q, we get: 
q = sqrt[(1/2)(35 N/m)(0.25 m)^2 / (1.0 × 10^−6 F)] = 0.025 C

Therefore, the initial charge on the capacitor is 0.025 C, which is answer choice C.

A 150-G Block on the End of a Spring with a Spring