Physics Homework help?

Question

a) What equal poistive charges would have to be placed on the earth and on the moon to neutralize their gravitational attraction?
b) Why don't you need to know the lunar distance to solve this problem? c) How many kilograms of hydrogen ions (protons) would be needed to provide the positive charge calculated in a)?


Thanks for any help :-) !!

Answer 1

gravitational attraction = electrostatic repulsion
GMm/d^2 = kQ^2/d^2
as you can see the d^2 cancel out. that is why lunar distance is irrelevant.
G is the universal gravitational constant. M is earth's mass, m is moon's mass, Q is charge on earth and moon. k is coulomb's constant.
solve equation for Q.
Q = sqrt (GMm/k)

divide the charge determined (Q) by the charge of a proton (1.602x10^-19) to determine the number of protons required.
multiply by mass of proton (1.673x10^-27kg) to determine mass of protons required.

Answer 2

a good way to get rid of physics homework
a) you need to equate the forces inorder to cancel them
gravitational force=G M m/r^2 where G universal gravitation constant, M mass of earth, m mass of moon, r lunar distance
coulombic force= k q^2 /r^2, k=1/(4 pi epsilon)
epsilon is the permittivity of free space
equate now
r^2 on both sides cancels, this answers b)
you can find the constants
q=((G M m)/(k))^(1/2)
c) a proton has a charge 1.6 e-19 c
whatever q you get divide the q by 1.6 e-19
that will give number of protons
next divide that by the avogadro number 6.023e23
that will give you in grams
again divide by thousand to get kilos

Answer 3

The gravitational attraction force is G*Me*Mm/d^2
The electric force is Qe*Qm/(1/4*π*e0*d^2)

To balance out, these must be equal

G*Me*Mm/d^2 = Qe*Qm/(1/4*π*e0*d^2). Note that the distance d appears in the denominator on both sides of the eq and therefore cancels out. If Qe and Qm are equal to Q, the charge is

Q = √[4*π*e0*G*Me*Mm]

Look up the values for earth mass Me, moon mass Mm, Newtonian gravitational constant G and permittivity of free space e0.