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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 a planet exerts on Earth is gravitational.

(a) Calculate the gravitational force Father 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 F Jupiter on the baby due to Jupiter if it is at its closest distance to Earth, some 6.29 x 10^11 m away.
(c) How does the force of Jupiter on the baby compare to the force of the father on the baby Father / OF Jupiter

Respuesta :

cryssatemp

Answer: (a)[tex]F=7(10)^{-7}N[/tex]

              (b)[tex]F=1.344(10)^{-6}N[/tex]  

              (c) The force of Jupiter on the baby is slightly greater than the the force of the father on the baby.

Explanation:

According to the law of universal gravitation, which is a classical physical law that describes the gravitational interaction between different bodies with mass:

[tex]F=G\frac{m_{1}m_{2}}{r^2}[/tex]   (1)

Where:

[tex]F[/tex] is the module of the force exerted between both bodies

[tex]G[/tex] is the universal gravitation constant and its value is [tex]6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex]

[tex]m_{1}[/tex] and [tex]m_{2}[/tex] are the masses of both bodies.

[tex]r[/tex] is the distance between both bodies

Knowing this, let's begin with the answers:

(a) Gravitational force Father exertes on baby

Using equation (1) and taking into account the mass of the father [tex]m_{1}=100kg[/tex], the mass of the baby [tex]m_{2}=4.20kg[/tex] and the distance between them [tex]r=0.2m[/tex], the force [tex]F_{F}[/tex]  exerted by the father is:

[tex]F_{F}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(100kg)(4.20kg)}{(0.2m)^2}[/tex]   (2)

[tex]F_{F}=0.0000007N=7(10)^{-7}N[/tex]   (3)

(b) Gravitational force Jupiter exertes on baby

Using again equation (1) but this time taking into account the mass of Jupiter [tex]m_{J}=1.898(10)^{27}kg[/tex], the mass of the baby [tex]m_{2}=4.20kg[/tex] and the distance between Jupiter and Earth (where the baby is) [tex]r_{E}=6.29(10)^{11}m[/tex], the force [tex]F_{J}[/tex]  exerted by the Jupiter is:

[tex]F_{J}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(1.898(10)^{27}kg)(4.20kg)}{(6.29(10)^{11}m)^2}[/tex]   (4)

[tex]F_{J}=0.000001344N=1.344(10)^{-6}N[/tex]   (5)

(c) Comparison

Now, comparing both forces:

[tex]F_{J}=0.000001344N=1.344(10)^{-6}N[/tex]   and [tex]F_{F}=0.0000007N=7(10)^{-7}N[/tex]  we can see [tex]F_{J}[/tex] is greater than [tex]F_{F}[/tex]. However, the difference is quite small as well as the force exerted on the baby.