Coulombs Law is KILLING ME

[lalablu3]

Homework Statement

You remove two socks from a hot dryer and find that they repel with force of 0.002 N when they’re 1 cm apart. If they have equal charges, and you separate the socks until they’re 5 cm apart, what force will each sock exert on the other? Round the answer to 3 significant digits.

Homework Equations

F=8.9*10^9(q1)(q2) / r^2

The Attempt at a Solution

Ive been working on this for over an hour and am frieking out! First I try to solve for the two charges, using .1 (1cm-converted to meter). I know that once I get this, I can use it to change .1 to .5 and solve for F. Problem is I have been having trouble solving for Q! which leaves me stuck in the begining.

Please please help, I've got a midterm in the morning.

 

[Abraham]

F=kq1q2/r^2

at .01m, F = .002
Solve for q^2, since q1 = q2
q^2= (0.002)(.01^2) / (8.9e+9)
= 2.25e-17 C
so q1 or q2 equals the square root of q^2:
(2.25e-17)^0.5 = 4.74e-9 C

Then, use these values to solve if r = .05 (just plug them back into the equation)

I hope this helped

 

[Moetasim]

Don't panic! It's completely normal to get stuck on a problem for a while, especially when it involves a new concept like Coulomb's Law. Take a deep breath and let's break this down step by step.

First, let's review Coulomb's Law: F=8.9*10^9(q1)(q2)/r^2. This equation tells us that the force between two charged objects depends on the magnitude of their charges (q1 and q2) and the distance between them (r). In this case, we know the force (0.002 N) and the distance (1 cm or 0.01 m), and we are trying to find the charges.

To solve for the charges, we can rearrange the equation to q1=q2=F*r^2/8.9*10^9. Plugging in the values we know, we get q1=q2=0.002*0.01^2/8.9*10^9, which gives us a charge of 2.25*10^-11 C for each sock.

Now, to find the force when the socks are 5 cm apart, we can use the same equation and plug in the new distance (0.05 m) and the charges we just found. F=8.9*10^9*(2.25*10^-11)^2/(0.05)^2, which gives us a force of 2.52*10^-5 N for each sock. Remember to round to 3 significant digits, so our final answer is 2.52*10^-5 N for each sock.

I hope this helps clear things up for you. Remember to take your time and double check your calculations. Good luck on your midterm!