The gravitational force between two electrons that are 0.98 m apart is 5.64 10-71 N. Find the mass of an electron. (Use G = 6.67 10-11 N·m2/kg2.)

Do you use F=G(m1*m2)/r^2???

Yes, with m1 and m2 the same mass of the electron.

So then would you put

(m1*m2)=F*r^2/G

and then the answer to the right side of the equal sign, would be divided by 2??

If m1=m2, then

m^2=F/G * r^2
take the square root of each side.

Yes, you are correct! To calculate the gravitational force between two objects, you can use the formula:

F = G * (m1 * m2) / r^2

where:
- F is the gravitational force between the objects,
- G is the gravitational constant (6.67 * 10^-11 N·m^2/kg^2),
- m1 and m2 are the masses of the two objects, and
- r is the distance between the two objects.

In this case, you are given the gravitational force (F) between two electrons, which is 5.64 * 10^-71 N, and the distance (r) between them, which is 0.98 m. You need to find the mass (m1 or m2) of an electron.

To rearrange the formula and solve for the mass of an electron, we can isolate the mass:

F = G * (m1 * m2) / r^2

Multiply both sides by r^2:

F * r^2 = G * (m1 * m2)

Divide both sides by G:

(m1 * m2) = (F * r^2) / G

Now, substitute the given values:

(m1 * m2) = (5.64 * 10^-71 N) * (0.98 m)^2 / (6.67 * 10^-11 N·m^2/kg^2)

Since both electrons have the same mass (m1 = m2 = me), we can simplify further:

m^2 = (5.64 * 10^-71 N) * (0.98 m)^2 / (6.67 * 10^-11 N·m^2/kg^2)

Now, take the square root of both sides to solve for the mass:

m = √[(5.64 * 10^-71 N) * (0.98 m)^2 / (6.67 * 10^-11 N·m^2/kg^2)]

Calculating this expression gives you the mass of an electron.