Question

there are 3 objects of masses 6kg, 4kg, 2kg respectively. if the 2nd object is 20m east if th 1st object and the 3rd object is 10m south of the 1st object what is the magnitude & direction of the gravitational force exerted on the 1st object

Answer 1

Gravutational Force ,$F=Gm_{1}m_{2}/r^{2}$

where $G=6.674*10^{-11}Nm^{2}/kg^{2}$

$F_{2}=Gm_{1}m_{2}/r^{2}$

$F_{2}=6.674*10^{-11} *6kg*4kg/(20m)^{2}$

$F_{2}=6.674*10^{-11} *6*4/20^{2}$

$F_{2}=4*10^{-12}N$

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$F_{3}=Gm_{1}m_{3}/r^{2}$

$F_{3}=6.674*10^{-11} *6kg*2kg/(10m)^{2}$

$F_{3}=6.674*10^{-11} *6*2/10^{2}$

$F_{3}=8*10^{-12}N$(downwards)

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Net Force,$F=\sqrt{F_{2}^{2}+F_{3}^{2}}$

$F=\sqrt{(4*10^{-12})^{2}+(8*10^{-12})^{2}}$

ANSWER: $F=8.944*10^{-12}N$

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Direction

$tan\theta =F_{3}/F_{2}$

$\theta =tan^{-1}(F_{3}/F_{2})$

$\theta =tan^{-1}(-8*10^{-12}/4*10^{-12})$

$\theta =-63.435^{\circ}$

$\theta =360^{\circ}-63.435^{\circ}$

ANSWER: $\theta =293.57^{\circ}$ counter clockwise

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