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Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one’s birth. The only known force that a planet could exerts on us is gravitational, so if there is anything to astrology we should expect this force to be significant.

(a) Calculate the gravitational force exerted on a 4.20-kg baby by a 100-kg father 0.200 m away at birth (he is assisting, so he is close to the child).

(b) Calculate the force on the baby due to Jupiter if it is at its closest distance to Earth, some
6.29×1011m
away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)

Answer :

Answer:

[tex]F_f=7.0035\times 10^{-7}\ N[/tex]

[tex]F_j=8.45\times 10^{-6}\ N[/tex]

Explanation:

(a)

  • mass of baby, [tex]m_b=4.2\ kg[/tex]
  • mass of father, [tex]m_f=100\ kg[/tex]
  • distance between father and baby, [tex]d=0.2\ m[/tex]

Now, the gravitational force on baby due to father:

[tex]F_f=G \frac{m_b.m_f}{d^2}[/tex]

[tex]F_f=6.67\times 10^{-11}\times \frac{4.2\times 100}{0.2^2}[/tex]

[tex]F_f=7.0035\times 10^{-7}\ N[/tex]

(b)

  • distance between baby and Jupiter, [tex]r=6.29\times 10^{11}\ m[/tex]
  • We have mass of Jupiter, [tex]m_j=1.898\times 10^{27}\ kg[/tex]

Now, the gravitational force on baby due to planet Jupiter:

[tex]F_j=G \frac{m_b.m_j}{r^2}[/tex]

[tex]F_j=6.67\times 10^{-11}\times \frac{4.2\times 1.898\times 10^{27}}{(6.29\times 10^{11})^2}[/tex]

[tex]F_j=8.45\times 10^{-6}\ N[/tex]

We find that the gravitational force due to Jupiter is considerably greater than the force due to mass of father.

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