Calculating Closest Approach Distance for Two Moving Protons

  • Thread starter kdrobey
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In summary, the problem involves two protons moving towards each other with initial speeds of 2.1 x 10^6 m/s. The goal is to determine the distance of closest approach. The equation used is 1/2mVo^2 = Kq^2/r, where both protons' kinetic energy must be set equal to their potential energy. After some attempts and using the correct formula, the final answer is 9.6e-14.
  • #1
kdrobey
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Homework Statement



Two Protons are moving directly toward one another. When they are very far apart, their initial speeds are 2.1 x 10^6 m/s. What is the distance of closest approach?

Homework Equations





The Attempt at a Solution

 
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  • #2
Show what you've done so far.

Hint: What's conserved?
 
  • #3
Your are expected to show an attempt at the problem. What are your thoughts on the problem?
 
  • #4
ok, will do
 
  • #5
Okay I have the same problem except my initial speed is 1.2*10^6

So, I used the equation 1/2mVo^2 = Kq^2/r

I am solving for r and I keep getting 1.92 * 10^-13, but it is wrong. What am I doing wrong?
 
  • #6
Realize that both protons are moving and thus have kinetic energy.
 
  • #7
So, I am using the wrong formula? Not getting it...
 
  • #8
You need to set total KE equal to PE.
 
  • #9
I thought that is what I did
 
  • #10
What's the KE of each proton? (Symbolically--no need for numbers yet.)
 
  • #11
I am not sure what you are looking for
 
  • #12
nckaytee said:
I am not sure what you are looking for
The basic expression for the KE of each proton, like you used in post #5.
 
  • #13
1/2mVo^2
 
  • #14
nckaytee said:
1/2mVo^2
Good. That's the KE of one proton. So what's the total KE of both protons?
 
  • #15
so,

1/2mVo^2 + 1/2mVo^2= Kq^2/r

?
 
  • #16
Good.
 
  • #17
Okay I got the correct answer 9.6e-14 ... finally :-)
 

FAQ: Calculating Closest Approach Distance for Two Moving Protons

What is the distance of closest approach?

The distance of closest approach, also known as the minimum approach distance, is the shortest distance between two objects during their interaction or motion. It is often used to describe the closest point at which two bodies come near each other, such as the closest distance between a planet and its moon.

How is the distance of closest approach calculated?

The distance of closest approach is typically calculated using mathematical equations, such as the Law of Universal Gravitation or the Coulomb's Law, depending on the type of interaction between the objects. These equations take into account the masses, velocities, and distances of the objects to determine the minimum distance between them.

Why is the distance of closest approach important in science?

The distance of closest approach is important in science because it allows us to understand and predict the behavior of objects in motion or interaction. It is particularly useful in fields such as astronomy, physics, and chemistry to study the dynamics of celestial bodies, particles, and molecules.

Can the distance of closest approach change over time?

Yes, the distance of closest approach can change over time. This is because the positions and velocities of objects can change due to various factors, such as gravity, acceleration, or external forces. In some cases, the distance of closest approach may decrease over time, leading to a collision between the objects.

How is the distance of closest approach related to impact parameter?

The impact parameter is the perpendicular distance between the path of an object and a point of reference, such as the center of another object. It is often used in conjunction with the distance of closest approach to determine the likelihood of a collision or interaction between the two objects. The smaller the impact parameter, the closer the distance of closest approach and the higher the chance of a collision.

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