Two tiny metal spheres A and B of mass m_A = 4.17 g and m_B = 13.5 g have equal
ID: 3162465 • Letter: T
Question
Two tiny metal spheres A and B of mass m_A = 4.17 g and m_B = 13.5 g have equal positive charges q = 3.87 mu C. The spheres are connected by a massless nonconducting string of length d = 1.44 m, which is much greater than the radii of the spheres. (a) What is the electric potential energy of the system? Suppose you cut the string. At that instant, what is the acceleration of (b) sphere A and (c) sphere B? A long time after you cut the string, what is the speed (d) sphere A and (e) sphere B? Number Units Number Units Number Units Number Units Number UnitsExplanation / Answer
a) mA = 4.17 gm
mB = 13.5 gm
q = 3.87 uC
potential energy of system = k * q^2/d
potential energy of system = 9 *10^9 * (3.87 *10^-6)^2/1.44
potential energy of system = 0.094 J
part d)
after a very long time
Using conseration of energy
0.5 * 4.17 *10^-3 * v1^2 + 0.5 * 13.5 *10^-6 * v2^2 = 0.094 ----(1)
4.17 * v1 - 13.5 * v2 = 0 -----(2)
solving for v1 and v2
v1 = 6.71 m/s
v2 = 2.07 m/s
the speed of sphere A is 6.71 m/s
e) the speed of sphere B is 2.07 m/s
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