Part (a) of the figure shows a particle A that can be moved along a y axis from
ID: 1445429 • 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 0.3220 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
Let mass of B and C are M each and that of A be m.
- GMM/2D -2GMm/sqrt { D^2 + y^2} =U
When y=0,
-GMM/2D -2GMm/D = -3.5 × 10^-10 J
6.67×10^-11MM/(2×0.322) -2×6.67 ×10^-11×Mm/0.322 = 3.5 ×10^-10
10.36MM+ 41.43 Mm = 35.....equation1
when y = infinity
10.36 MM =2.7
M=0.51 kg
Solving equation 1,
41.43 Mm =35 -2.7 =32.3
m = 32.3/(41.43 ×0.51) = 1.53 kg
A)Mass of particles B and C =0.51 kg
B) Mass of particles A =1.53 kg