A 69.0-g block carrying a charge Q = 39.0 C is connected to a spring for which k
ID: 1572509 • Letter: A
Question
A 69.0-g block carrying a charge Q = 39.0 C is connected to a spring for which k = 71.0 N/m. The block lies on a frictionless, horizontal surface and is immersed in a uniform electric field of magnitude E = 4.68 104 N/C directed as shown in the figure below. The block is released from rest when the spring is unstretched (x = 0).
(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.
2k·A2Q
position cm amplitude cm m, Q.Explanation / Answer
a)
conserving energy
work done by electric field is stored as potential energy of spring
QE x = 0.5 x^2
x = 2QE/k = 0.0514m
x = 5.14c,
b)
equilibrium position
xe = QE/k = 2.57 cm
amplitude
A = QE/k = 2.57cm
c)
(V1-V2 )xQ = 0.5 k (2A)^2
V1-V2 = 2kA^2 /Q
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