1. Two small silver spheres, each with a mass of 8.00 g, are separated by 1.00 m. ?

Question

1. Two small silver spheres, each with a mass of 8.00 g, are separated by 1.00 m. Calculate the fraction of the electrons in one sphere that must be transferred to the other to produce an attractive force of 1.00 104 N (about 1 ton) between the spheres.

(The number of electrons per atom of silver is 47, and the number of atoms per gram is Avogadro's number divided by the molar mass of silver, 107.87 g/mol.)

I keep trying to solve this promblem, however I keep coming up with an incredibly small and apprantly correct answer. After applying the force and the coloumbs constant(9 * 10^9), and diving by Avragados number (6.02214158 * 10^23) and the constant, I found the answer to be (.000001093). I dont understand where I am going wrong.

2. Two small beads having positive charges 10q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin (the location of the larger charge) to the point x = d. As in Figure P23.10, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium?

x = __d.

After applying to algebra to the equation

[(k*10q*Q)/(x^2)] = [(k*q*Q)/(d-x^2)] I end up with x=.5d. Once again, I have no idea what i am doing wrong. Please help!!

Answer 1

ANSWER TO # 2

(K * 10q * Q)/x^2  =  K * q * Q)/(d-x)^2  

cancelling common terms => 10/ = (d-x)^2

cross multiply => 10* (d-x)^2 = x^2

sq rt both sides => 3.16 * (d-x) = x

solving => 3.16d=4.16x => x = 0.76d

let me knowwhat you think.

Answer 2

2. I think you got rid of the 10 on the left hand side. If you do that then you will get the answer you got.

[(k*10q*q)/(x^2)] = [(k*q*q)/(d - x)^2]

10/x^2 = 1/(d - x)^2

SQRT(10)(d - x) = x

x[1 + SQRT(10)] = d[SQRT(10)]

x = d*SQRT(10)/[1 + SQRT(10)]

x = (0.76)d

1. For one thing the force is not about 1 ton. I see 1.00104 N and that is just about 1 N and that corresponds to about 0.2248 lbs of force. So either the number is a typo or the 1 ton is some sort of error. I think I will ignore the decimal point and use 100104 N as the force.

N = number of electrons per sphere

N = (#electrons/atom)(weight)(number of atoms/gm)

N = 47*8*(6.02214158 * 10^23) /107.87

N = 2.0991x10^24 electrons

F = k*q*q/d^2

d = 1 meter

k = 9x10^9 N • m^2 / C^2

F = 100104 N

q^2 = F*d^2/k

q = SQRT(F*d^2/k)

q = SQRT(11.1226x10^-6)

q = 3.335066x10^-3 C

charge of an electron = 1.60217646x10^-19 C

So q corresponds to about 2.08158x10^16 electrons

fraction of electrons = 2.08158x10^16 / 2.0991x10^24

fraction = 0.99165x10^-8 = 9.9165x10-9

This fraction is even smaller than yours so let me know if you see anything wrong, I will be keeping an eye on this.