Principle of Energy Conservation for Two Protons?

In summary, to collide two protons, they must have an initial speed of 8.3E6 m/s and a minimum kinetic energy of 1/2 mv^2.
  • #1
musiliu
44
0

Homework Statement



Two protons (radius 10^-15 m) are headed directly toward each other with
equal speeds. Use the principle of energy conservation to compute the minimum
kinetic energy and initial speed each proton must have if they are to
collide.

Homework Equations


W = delta K
W = - delta U
U1 + K1 = U2 + K2

The Attempt at a Solution


I've tried drawing diagram and listing known equations but for some reason, i just can't do this..need some good tips or hints...
 
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  • #2
musiliu said:

Homework Statement



Two protons (radius 10^-15 m) are headed directly toward each other with
equal speeds. Use the principle of energy conservation to compute the minimum
kinetic energy and initial speed each proton must have if they are to
collide.

Homework Equations


W = delta K
W = - delta U
U1 + K1 = U2 + K2

The Attempt at a Solution


I've tried drawing diagram and listing known equations but for some reason, i just can't do this..need some good tips or hints...

Well firstly, you would need to consider the collision as elastic, so conservation of momentum would play a role as well.

Conservation of KE will give one equation and conservation of momentum will give another equation. Form these two equations.
 
  • #3
ok, for conservation of momentum i got:

mvi1 + mvi2 = mvf1 + mvf2 (vi is initial and vf is final)

and i am not sure exactly what the conservation of KE is.. is it:

(1/2 mvi1)^2 + (1/2 mvi2)^2 = (1/2 mvf1)^2 + (1/2 mvf2)^2

I am not sure what the values of initial and final velocities are.. the question does not say they start out at rest.

Also, this question is from an Electromagnetism Physics class right before we learned about electric potential.. so I am not sure why the teacher gave us this problem, but I always suffered in Mechanics and was not good at it at all...
 
  • #4
Do you know the formula for electrical potential energy? (not potential, but potential energy)
 
  • #5
yes, the electric potential energy is kqQ / r

also, for the 2 equations i wrote, i came up with vi = vf.. and I have no idea what to do with this result..since the mass and and initial velocity of each proton is the same, i just kept canceling out variables..

but I still don't understand how to solve this problem, what do i do with vi = vf?

i don't understand what i am trying to find: what is "minimum kinetic energy" and initial speed the proton must have to collide?
 
  • #6
OK, i got help from a tutor, and this is how i solved the problem:

i used the potential energy at collision : U = kq^2 / 2R , where R is the radius of the proton
and then i set potential energy = kinetic energy of system

mv^2 = kq^2 / 2R

and found minimum v = 8.3E6 m/s and minimum KE for each proton = 1/2 mv^2 = 5.8E-14 J

is this answer and strategy correct?
 
  • #7
Yep, that's the right way to do it.
 

FAQ: Principle of Energy Conservation for Two Protons?

What is the Principle of Energy Conservation for Two Protons?

The Principle of Energy Conservation for Two Protons states that the total energy of a system consisting of two protons remains constant over time, regardless of any internal changes or interactions. This means that energy cannot be created or destroyed, only transferred or transformed between the two protons.

How does the Principle of Energy Conservation apply to two protons?

The Principle of Energy Conservation applies to two protons because they are both fundamental particles that carry a charge and have a mass. As such, they interact with each other through electromagnetic forces and can exchange energy, but the total energy of the system will always remain constant.

What is the significance of the Principle of Energy Conservation for Two Protons?

The Principle of Energy Conservation is a fundamental law of physics and has many important applications, including understanding the behavior of atomic and subatomic particles, predicting the outcomes of nuclear reactions, and explaining the stability of matter.

What are some examples of how the Principle of Energy Conservation is demonstrated in nature?

One example is the fusion of two protons in the core of the Sun, which releases energy in the form of light and heat. Another example is the decay of a radioactive isotope, where the energy released by the decay is distributed between the two resulting particles, in accordance with the Principle of Energy Conservation.

Is the Principle of Energy Conservation for Two Protons always applicable?

Yes, the Principle of Energy Conservation applies to all interactions between two protons, as well as interactions between any other particles in the universe. It is a universal law that has been extensively tested and confirmed through experiments and observations.

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