Find the order of magnitude of the electrostatic force

[mm2424]

Homework Statement

Two engineering students, John with a mass of 90 kg and Mary with a mass of 45 kg, are 30 m apart. Suppose each has a 0.01% imbalance in the amount of positive and negative charge, with one student being positive and the other negative. Find the order of magnitude of the electrostatic force of attraction between them by replacing each student with a sphere of water having the same mass as the student.

Homework Equations

F = kq1q2/r^2

The Attempt at a Solution

I solved this problem by finding the total number of protons and positive charge associated with them in John:

90000 g / 18 g/mol = 5000 mol x Avogadro's number = 3.01 x 10^27 molecules
then I multiplied by 10 protons/molecule to get 3 x 10^28 protons.
I multiplied this by the charge of a proton and got 4.82 x 10^9 C.
I multiplied by 0.0001 and got 482202 C of positive charge.

I did the same for Mary and got 240000 C of negative charge.

When plugged into the electrostatic force equation, I got 1.16 x 10^18 N.

However, in my professor's answer key, after he finds the number of water molecules, he multiplies by 18 and not 10. It seems like a mistake to me, but am I missing something? Should I multiple by 10 or 18 in this step?

Thanks!

 

[PeterO]

Homework Statement

Two engineering students, John with a mass of 90 kg and Mary with a mass of 45 kg, are 30 m apart. Suppose each has a 0.01% imbalance in the amount of positive and negative charge, with one student being positive and the other negative. Find the order of magnitude of the electrostatic force of attraction between them by replacing each student with a sphere of water having the same mass as the student.

Homework Equations

F = kq1q2/r^2

The Attempt at a Solution

I solved this problem by finding the total number of protons and positive charge associated with them in John:

90000 g / 18 g/mol = 5000 mol x Avogadro's number = 3.01 x 10^27 molecules
then I multiplied by 10 protons/molecule to get 3 x 10^28 protons.
I multiplied this by the charge of a proton and got 4.82 x 10^9 C.
I multiplied by 0.0001 and got 482202 C of positive charge.

I did the same for Mary and got 240000 C of negative charge.

When plugged into the electrostatic force equation, I got 1.16 x 10^18 N.

However, in my professor's answer key, after he finds the number of water molecules, he multiplies by 18 and not 10. It seems like a mistake to me, but am I missing something? Should I multiple by 10 or 18 in this step?

Thanks!

I like your 10.

Perhaps your professor was thinking of an oxygen molecule plus a water molecule, rather than a water molecule??