How Many Electrons Are Needed to Accelerate Two Charged Spheres at 25g?

[flynnk567]

I know almost this exact thing has been asked before but even after looking at the other posts I still can't figure out what I'm doing wrong.

Homework Statement

Two very small 8.05-g spheres, 11.0 cm apart from centre to centre, are charged by adding equal numbers of electrons to each of them. Disregarding all other forces, how many electrons would you have to add to each sphere so that the two spheres will accelerate at 25.0g when released?

Homework Equations

F=ma
F=k(q1q2/r^2)
q=ne

The Attempt at a Solution

F=ma=F=k(q1q2/r^2)

F= (8.05g)(25)(9.8m/s)=1972.25

1972.25(.11m)^2=(8.987e9)Q^2

(23.86)/(8.987e9)=Q^2

Sqrt(2.66e-9)=Q

5.15e-5=Q

Q=ne

n=5.15e-5/1.6e-19

=3.22e14 electrons

 

[Tsunoyukami]

What exactly are you asking us to do? Are you getting the wrong final answer?

I would recommend double-checking to make sure you've used the correct units for your calculations - in particular you need to convert the mass from grams to kilograms before doing anything else.

 

[flynnk567]

I converted mass to kg and mastering physics still said I was wrong but now it was close enough for them to just think it was a rounding or sig fig error. It was my last attempt so they showed the correct answer was 1.02e13 and I got 1.71e12. I'm sure I probably typed something wrong into my calculator, thanks for you help though :)

 

[ap123]

You should repeat your initial calculations using kg instead of g (as pointed out in post #2).
You will then get the correct answer.

 

[Nickie]

First of all, it is important to note that Coulomb's Law deals with the electrostatic force between charged particles, not their acceleration. For acceleration, we need to use Newton's Second Law, F=ma.

In this problem, we are given the masses and distance between the two spheres, and we need to find the number of electrons on each sphere that will cause them to accelerate at 25.0g when released.

To solve this, we can use the equation F=ma, where F is the force of attraction between the two spheres, m is the mass of each sphere, and a is the acceleration (25.0g in this case).

We can then use Coulomb's Law, F=k(q1q2/r^2), to find the value of F. Here, k is the Coulomb's constant, q1 and q2 are the charges on each sphere, and r is the distance between them.

Substituting the given values, we get:

F=ma=1972.25= k(q^2/0.11^2)

Rearranging the equation, we get:

q=sqrt(1972.25*0.11^2/8.987e9)

=5.15e-5C

Since q=ne, where n is the number of electrons, we can find the number of electrons on each sphere by dividing this value by the charge of one electron (1.6e-19C).

n=5.15e-5C/1.6e-19C

=3.22e14 electrons

Therefore, to cause the two spheres to accelerate at 25.0g when released, we need to add 3.22e14 electrons to each sphere.