A 66.0-g block carrying a charge Q = 36.0 C is connected to a spring for which k

Question

A 66.0-g block carrying a charge Q = 36.0 C is connected to a spring for which k = 70.0 N/m. The block lies on a frictionless, horizontal surface and is immersed in a uniform electric field of magnitude E = 4.88 104 N/C directed as shown in the figure below. The block is released from rest when the spring is unstretched (x = 0).

(a) By what maximum distance does the block move from its initial position?

______cm

(b) Find the subsequent equilibrium position of the block and the amplitude of its motion. (Indicate the direction with the sign of your answer.) position cm amplitude

_______cm

(c) Using conservation of energy, find a symbolic relationship giving the potential difference between its initial position and the point of maximum extension in terms of the spring constant k, the amplitude A, and the charge Q. V = ______

Explanation / Answer

m = 66 g = 66 * 10-3 kg

Q = 36 * 10-6 C

a) F = E Q

x = 2 E Q / k = (2 * 4.88 * 104 * 36 * 10-6) / (70) = 5.00 cm

b) Amplitude A = QE/k = (4.88 * 104 * 36 * 10-6) / (70) = 2.50 cm

c) V = 2 Q E2 / k = (2 * (4.88 * 104)2 * 36 * 10-6) / (70) = 2450 volts

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