Gravitational force between 2 protons

[jace]

1. Calculate the electric force between 2 protons in a nucleus that are 5*[10]^{-15} m apart. Compare this with the gravitational force between them.

Homework Equations

F(sub g)={GM(sub 1)M(sub 2)}/r^(2)

G=6.67*10^(-11) Nm^(2)/kg^(2)

Mass of proton=1.67*10^(-27)Kg

The Attempt at a Solution

i computed the gravitational force between the two protons, i think, but the asks why might they make you wonder why the protons don't fly apart. I think i may have computed the gravitational force wrong...

also how do make the formatting buttons work so i can show my equations and haphazard work?

 

[HallsofIvy]

Have you shown that the two protons attract?! Have you also calculated the repelling force of the two positively charged protons at the same distance?

As far as formatting is concerned you can use such html things as [ sup ]2[ /sup ] for superscripts (x²), [ sub ]1[/ sub ], for subscripts (a₁), [ b] a [ /b ] for bold face (a) etc.

You can also use "LaTex" using the [ tex ] and [ /tex ] tags. You can click on any LaTex equations to see the codes used or click on "quote" to see both the latex and html codes. Finally, there is a "LaTex tutorial" in the tutorials section of the Science Education forum.

 

[Moetasim]

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First of all, let's calculate the electric force between two protons. This can be done using the Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The equation for this is:

F(sub e) = k(q1*q2)/r^(2)

Where k is the Coulomb's constant (8.99*10^9 Nm^2/C^2), q1 and q2 are the charges of the two protons (which are equal since they are both protons), and r is the distance between them. Plugging in the values for these variables, we get:

F(sub e) = (8.99*10^9 Nm^2/C^2)(1.602*10^-19 C)^2/(5*10^-15 m)^2 = 9.12*10^-9 N

Now let's compare this with the gravitational force between the two protons. The equation for this is given by Newton's law of gravitation:

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

Where G is the gravitational constant (6.67*10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two protons (which we know from the given information), and r is the distance between them. Plugging in the values, we get:

F(sub g) = (6.67*10^-11 Nm^2/kg^2)(1.67*10^-27 kg)^2/(5*10^-15 m)^2 = 1.11*10^-47 N

Comparing these two forces, we can see that the electric force is much stronger than the gravitational force. In fact, it is approximately 10^38 times stronger!

So why don't the protons fly apart if the electric force is so much stronger? This is because there is another force at play here - the strong nuclear force. This force is responsible for binding the protons and neutrons together in the nucleus of an atom. It is much stronger than both the electric and gravitational forces, but it only acts over very short distances (on the order of 10^-15 m). Therefore, at the distance of 5*10^-15 m between the two protons, the strong nuclear force is dominating