86.2 Gravitational force of a uniform sphere on a particle The total force on m due to the entire shell R 2 f=dF nGtpmR rr+R +1)dx mM F nGtpmR (4R)=G Inside the shella F=dF nGtpmR R +1)dx 0 86.2 Gravitational force of a uniform sphere on a particle Exercise 1: Find the gravitational force between The small ball of mass m, and the thin staff of m and length l Solutio mdm dm dF=g dm= adr=-dr L F=[dF=( Gmm可:=cm L l dd+l M117 F=G d+L 88 §6.2 Gravitational force of a uniform sphere on a particle The total force on m due to the entire shell: ∫ ∫ + − + − = = r R r R x x r R r Gt mR F dF ( 1)d 2 2 2 2 π ρ 2 2 (4 ) r mM R G r Gt mR F = = π ρ Inside the shell: 0 ( 1)d d 2 2 2 2 = + − = = ∫ ∫ + − r R R r x x r R r Gt mR F F π ρ §6.2 Gravitational force of a uniform sphere on a particle Exercise 1: Find the gravitational force between The small ball of mass m1 and the thin staff of mass m and length L. Solution: r L m m r i r m m F G d d d ˆ d d 2 1 = = = λ r i L d d L m m i G r r L m m F F G d L d ˆ) 1 1 ( ˆ d d 1 2 1 + = = = − ∫ ∫ r r + i L d d L m m F G ˆ) 1 1 ( 1 + = − r F x r d