You will need the following information for this problem: 1) The force law for g

Question

You will need the following information for this problem:
1) The force law for gravitation is: Fg=GM1M2d2(G=6.67×10?11N×m2kg2)
where M1 and M2 are the masses of the two objects, d is the distance between them, and G is the gravitational constant. ("N" is the abbreviation for newton, the metric unit of force.)
2) The force law for electromagnetism is: FEM=kq1q2d2(k=9.0×109N×m2Coul2)
where q1 and q2 are the charges of the two objects (in Coulombs, the standard unit of charge), d is the distance between them, and k is a constant.("Coul" is an abbreviation for Coulomb.)
3) The charge of an electron is ?1.6×10?19Coul.
Suppose Earth and the Sun each had an excess charge equivalent to the charge of just 5 electrons.

Part A

Calculate the gravitational force between Earth and the Sun. (Hint: You'll need the following data about the Earth and Sun: MEarth=5.97×1024kg, MSun=1.99×1030kg, dbetween Earth and Sun=149.6×106km.)

Express your answer to three significant figures and include the appropriate units.

Part B

Calculate the electromagnetic force between Earth and the Sun.

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Part A.
Given The force law for gravitation is: Fg=GM1M2d2 where (G=6.67×10?11N×m2kg2)

The force law for gravitation is Fg = G*M1 * M2/d2

= 6.67* 10-11 * 5.97 * 1024 *1.99*1030 /(149.6×109 * 149.6 * 109) = 0.003540707 * 1025

Expressing it in three significant digits = 3.54*1022 N

Part B.
Now given 1 electron charge = -1.6*10-19 Coul
Thus charge of 5 electrons = 5 *  -1.6*10-19 Coul =  -8*10-19 Coul

Now force of electromagnetism = k * q1 * q2 / d2
Thus F = 9 * 109 *  -8*10-19 *  -8*10-19 / (149.6* 109 * 149.6 * 109 )
F = 0.0257370 * 10-47N

Thus F = 2.57 * 10 -49 N

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