a) $7.01 \times 10^{-7} \textrm{ N}$

b) $1.34 \times 10^{-6} \textrm{ N}$. The force of gravity due to Jupiter is greater than that of the father by a factor of $1.9$.

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View sample solution## Calculator Screenshots

This is College Physics Answers with Shaun Dychko. The force of gravity between the father and his newborn baby will be the gravitational constant, times the mass of the father, times the mass of the baby, divided by the distance between the father and the baby squared. So 6.673 times ten to the minus eleven times 100 kilograms, mass of the father, times 4.2 kilograms mass of the baby, divided by the 20 centimeters squared between the father and baby which we read in meters as 0.2 meters. This is 7.01 times ten to the minus seven Newtons which is a very small number, much smaller than the other forces the baby is experiencing during childbirth I can tell you. The force due to Jupiter is gravitational constant times the mass of Jupiter which is 1.898 times ten to the twenty-seven kilograms, multiplied by the mass of the baby divided by the distance between Jupiter and the earth at its closest, which is 6.29 times ten to the eleven meters, we square that. That gives 1.34 times ten to the six, negative six Newtons. The ratio between those two forces, force due to Jupiter and the force due to the father, is 1.34 times ten to the minus six divided by 7.01 times ten to the minus seven which is about 1.9. So the force of gravity due to Jupiter is greater than that of the father by a factor of 1.9. But even though the force due to Jupiter is two times greater than the force of gravity due to the father, this is still something that's negligible because it's two times greater than something that's really, really, really, really small.

## Comments

Submitted by bryanlovell on Tue, 09/18/2018 - 10:54

In the video @ 45 seconds you have (1.898*10^27) but on the calculator you just do (1.898^27) Can you still get the correct answer doing it like that?

Submitted by ShaunDychko on Tue, 09/18/2018 - 11:04

Hi bryanlovell, thanks for the question. With a closer look at the calculator screenshot, notice the capital "E" between 1.897 and 27. This is my favorite shorthand way of writing "times 10^". It has an advantage over typing "* 10^27" since the calculator understands that 1.897E27 should be treated as a single number. This means that when dividing by 1.897E27, the 10^27 factor stays in the denominator where it belongs with the 1.897 factor. To explain by example, for the problem $\dfrac{20}{10} = 2$, typing "20 / 1E1 = 2" which is correct, whereas "20 / 1 * 10^1 = 200" which is not the expected answer since the capital E wasn't used. Of course, one could type "20 / (1 * 10^1) = 2" to get the correct answer with brackets, but avoiding the trouble of typing those brackets is the whole point of the capital E shortcut.

I hope you enjoy the solutions,

Shaun

In reply to In the video @ 45 seconds… by bryanlovell