Electrical and gravitational forces of protons

[joel amos]

Homework Statement

At what distance between two protons are the electrical and gravitational forces equal?

Homework Equations

electromagnetic Force = k(Q1*Q2/r^2)
gravitational Force = G(m1*m2/r^2)

Constants:
k = 9.0*10^9 (N m^2/c^2)
G = 6.673 × 10^-11 (m^3 kg^-1 s^-2)
Charge of proton: 1.6*10^-19 C
Mass of proton: 1.67*10^-27 kg

The Attempt at a Solution

I solved the first equation for r^2. Then, I substituted the second equation in for force since electromagnetic and gravitational force are equal in this problem. This seems logical, no? The only problem is, when I solve for r, the r's cancel out... :_(

 

[tms]

At what value of $r$ does $kq^2 = Gm^2$?

 

[Leong]

Homework Statement

At what distance between two protons are the electrical and gravitational forces equal?

Homework Equations

electromagnetic Force = k(Q1*Q2/r^2)
gravitational Force = G(m1*m2/r^2)

Constants:
k = 9.0*10^9 (N m^2/c^2)
G = 6.673 × 10^-11 (m^3 kg^-1 s^-2)
Charge of proton: 1.6*10^-19 C
Mass of proton: 1.67*10^-27 kg

The Attempt at a Solution

I solved the first equation for r^2. Then, I substituted the second equation in for force since electromagnetic and gravitational force are equal in this problem. This seems logical, no? The only problem is, when I solve for r, the r's cancel out... :_(

When r approaches zero or when they are very close to one another, the gravitational force is as large as the electrical force. Both the forces approach infinity.
or
When r approaches infinity or when they are very far apart, the gravitational force and the electrical force approach zero.
Make sense? I'm not so sure.

 

[tms]

But they don't approach zero or infinity at the same rate.

 

[joel amos]

At what value of $r$ does $kq^2 = Gm^2$?

I believe that the question is: At what value of $r$ does $(kq^2)/r^2 = Gm^2/(r^2)$?

 

[VantagePoint72]

At what distance between two protons are the electrical and gravitational forces equal?

They're never equal.

The only problem is, when I solve for r, the r's cancel out...

That's why.

 

[joel amos]

They're never equal.

Okay, thanks!

 

[tms]

I believe that the question is: At what value of $r$ does $(kq^2)/r^2 = Gm^2/(r^2)$?

But, as you pointed out, the $r$s cancel.