Analytical Mech Homework Solutions 63

# Analytical Mech Homework Solutions 63 - CHAPTER 6...

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CHAPTER 6 GRAVITATIONAL AND CENTRAL FORCES 6.1 3 4 3 s mV r ρ ρπ == 1 3 3 4 s m r πρ  =   () 22 4 2 33 3 2 44 43 2 s Gmm Gm G Fm m r   =     2 1 2 3 3 4 FFG m m Wm g g 2 11 2 2 3 6 3 1 3 3 23 6.672 10 4 11.35 1 10 1 49 . 8 3 1 0 1 F N m kg g cm kg cm kg s g m π −− ×⋅ × ⋅ 3 × × 9 2.23 10 F W 6.2 (a) The derivation of the force is identical to that in Section 6.2 except here r < R. This means that in the last integral equation, (6.2.7), the limits on u are R – r to R + r. 1 4 Rr GmM r R Fd Rr s + =+ s 22 22 2 4 GmM R r R r Rr Rr R rR r R r + +− 2 20 4 GmM Fr R r R r Rr = +−− + =   (b) Again the derivation of the gravitational potential energy is identical to that in Example 6.7.1,
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