Part (a) of the figure shows a particle A that can be moved along a y axis from
ID: 1497450 • Letter: P
Question
Part (a) of the figure shows a particle A that can be moved along a y axis from an infinite distance to the origin. That origin lies at the midpoint between particles B and C, which have identical masses, and the y axis is a perpendicular bisector between them. Distance D is 0.3974 m. Part (b) of the figure shows the potential energy U of the three-particle system as a function of the position of particle A along the y axis. The curve actually extends rightward and approaches an asymptote of –2.7 x 10-11 J as y approaches infinity. What are the masses of (a) particles B and C and (b) particle A?
Explanation / Answer
(a) When A is at infinity, U = -GmB,C2/4D2= -2.7 * 10-11 J
=> mB,C = [2.7 * 10-11 * 4 * 0.39742 / (6.67 * 10-11)]1/2 = 0.51 kg
(b) Frm the graph, at y = 0.5 m, U = -2 * 10-11 J
=> -2GmAmB,C/(D2 + 0.52)1/2 = -2 * 10-11
=> mA = 10-11 * (0.39742 + 0.52)1/2 / [6.67 * 10-11 * 0.51] = 0.19 kg