Two identical objects each hold a net charge of q = 8e. If the gravitational force between the two objects exactly cancels the electrostatic force between the objects, what is the mass of each object?
Where G: 6.67E-11
Ke=8.99E9
I know the equation is
m=sqrt(ke*q^2/G)
yet when I plug everything in I got 2.52E11 which is incorrect.
Please help, I'm frustrated...
G M^2/R^ = Ke 64 e^2/R^2
M^2 = 64 Ke e^2/G
M = 8e sqrt(Ke/G)
You seem to be using the right formula, but I get a different numerical answer.
Are you sure you are using the right electron charge (e)?
Oh, you mean the 'e' in the 8e might stand for 8 times electron charge of 1.60217646E-19 coulombs? I was doing it as 8 times e(the mathematical constant 2.71828183)
Yes, e is the electron charge. You are comparing electrostatic and gravitational forces
Thank you! I should have known that, guess its getting late :)
I'm sorry you're feeling frustrated, but don't worry, let's work through this together and figure out what went wrong.
The equation you mentioned, m = sqrt(ke*q^2/G), is the correct equation to use for this problem. In order to solve it, we'll need to substitute the given values into the equation and calculate the mass of each object.
Given:
q = 8e (where e is the elementary charge, approximately 1.6E-19 C)
G = 6.67E-11 N(m/kg)^2
Ke = 8.99E9 N(m^2/C^2)
To avoid any issues with units, let's convert q to coulombs:
q = 8e * 1.6E-19 C/e
q = 1.28E-18 C
Now let's substitute the values into the equation and solve for m:
m = sqrt((Ke * q^2) / G)
m = sqrt((8.99E9 N(m^2/C^2) * (1.28E-18 C)^2) / 6.67E-11 N(m/kg)^2)
Now, let's calculate this value step by step:
m = sqrt((8.99E9 * (1.6E-18)^2) / 6.67E-11)
m = sqrt((8.99 * 2.56E-36) / 6.67E-11)
m = sqrt(2.28544E-35 / 6.67E-11)
m = sqrt(3.43079E-25)
m = 5.859E-13 kg
So, the mass of each object is approximately 5.859E-13 kg.
Please double-check the calculations and make sure you're using the correct values for the variables. If you have any further questions or need additional assistance, feel free to ask!