Chapter 13, Problem 042 Part (a) of the figure shows a particle A that can be mo

Question

Chapter 13, Problem 042 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 8 and C, which have identical masses, and the y axis is a perpendicular bisector between them. Distance D is 0.3982 m. Part (b) of the figure shows the potential energy U o the three-partidle system as a function of the position of partice A elong the y axis. The curve actualy extends rightward and approaches an asymptote of -2.7 x 10'11 as y approaches infinity. What are the masses of (a) particles 8 and C and (b) partice A? y (m) 1.5 -1 -3 (e) Number (b) Number akk ?, you would like to show work for this questioni Units Usits: aensomwork

Explanation / Answer

a )

given

D = 0.3982 m

U = - 2.7 X 10-11 J

using U = - G m m / 2D

- 2.7 X 10-11 = - 6.67 X10-11 m2 / 2 X 0.3982

2.7 = 6.67 m2 / 0.7964

m2 = 2.7 X 0.7964 / 6.67

m = 0.567 kg

b )

U = - (G m/D) ( m/2 + 2 mA )

- 3.4 X 10-11 = - (G m/D) ( m/2 + 2 mA )

3.4 X 10-11 = (6.67 X 10-11 X 0.567/0.3982) ( 0.567/2 + 2 mA )

( 0.2835 + 2 mA ) = 0.357

mA = 0.0735 / 2

mA = 0.03675 kg

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