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Chapter 13: Q42P (page 381)

Figure 13-46a shows a particleAthat can be movedalong ay-axis from an infinite distance to the origin. That origin liesat the midpoint between particlesBandC, which have identical masses, and theyaxis is a perpendicular bisector between them.DistanceDis0.3057m. Figure 13-46b shows the potential energyUof the three-particle system as a function of the position of particleAalong theyaxis. The curve actually extends rightward and approaches an asymptote of-2.7脳1011Jas鈫�鈭�. What are themasses of (a) particlesBandCand (b) particleA?

Short Answer

Expert verified
  1. Masses of particlesB and C are 0.50kg.
  2. Mass of particle A is 1.5kg.

Step by step solution

01

Step 1: Given

Distance,D is0.3057m

02

Determining the concept

Using the formula for gravitational potential energy, find the masses of particles B, C, and A for an infinitely large distance y and y = 0.

The formula is as follows:

U=-GMmR

where, m, and M are masses, R is the radius, G is gravitational constant and U is potential energy.

03

(a) Determining themasses of particles B and C

Now,

U=-GMmR

Applying the Pythagorean Theorem to a graph gives,

U=-GM22D+2GmMy2+D2

where M is the mass of particles B and C is the mass of a particle A .

For an infinitely large term,

2GmMy2+D2=0D=0.3057mU=-GM22DM=0.50kg

Therefore, the masses of a particle BandC are 0.50kg.

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