# Can Two Protons Have the Same Speed After an Elastic Collision?

• Mustard
In summary, the equation m1v1i + m2v2i = (m1+m2)vf is used to calculate the final velocity (vf) of two objects with masses m1 and m2 in an elastic collision. Using the given values, we can simplify the equation to (0.5)(v1i) = vf, showing that the final velocity will be half of the initial velocity of the first object. This also means that the second object will come to a complete stop after the collision. It is not possible for both objects to have the same speed after the collision in this scenario.
Mustard
Homework Statement
1) A proton, moving with a velocity of v initial in the x direction collides elastically with another proton that is initially at rest. Assuming that the two protons have equal speeds after the collision, find (a) the speed of each proton after the collision in terms of v initial and
(b) the direction of the velocity vectors after the collision.
Relevant Equations
Equations for first problem:
m1v1i + m2v2i = (m1+m2)vf
v1i + v1f = v2i + v2f
and we know v1f = v2f
m2v2i = 0 since 2nd proton is initially at rest
mass of proton = (1.67 × 10^-27) kg
m1v1i + m2v2i = (m1+m2)vf
(1.67 × 10^-27)v1i = (1.67 × 10^-27 + 1.67 × 10^-27) vf
(1.67 × 10^-27/3.34 × 10^-27)v1i = (3.34 × 10^-27/3.34 × 10^-27) vf
(1.67 × 10^-27/3.34 × 10^-27)v1i = vf
(0.5)(v1i) = vf

not sure what to do from here nor if I'm in the correct path ?

Hmm. About the question: an elastic collision between equal masses where one is initially at rest at the start will result in the other one coming to rest, and the one that was at initially rest moving off at the same speed. Is it possible for both to have the same speed after the collision? I don't think so...

## 1. Can two protons have the same speed after an elastic collision?

Yes, two protons can have the same speed after an elastic collision. In an elastic collision, the total kinetic energy of the system is conserved, meaning that the total energy before the collision is equal to the total energy after the collision. This means that the protons can exchange energy and momentum during the collision, resulting in them having the same speed.

## 2. What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision. In an elastic collision, the objects involved exchange energy and momentum without any loss of energy.

## 3. How does the speed of two protons change after an elastic collision?

The speed of two protons after an elastic collision depends on their initial speeds and masses. In an elastic collision, the objects involved exchange energy and momentum without any loss of energy. This means that the final speeds of the protons will depend on their masses and initial speeds.

## 4. What factors affect the speed of two protons after an elastic collision?

The speed of two protons after an elastic collision can be affected by factors such as their masses, initial speeds, and the angle at which they collide. The conservation of energy and momentum also play a role in determining the final speeds of the protons.

## 5. Can the speed of two protons ever be exactly the same after an elastic collision?

It is possible for the speed of two protons to be exactly the same after an elastic collision, but it is not guaranteed. In an elastic collision, the objects involved exchange energy and momentum without any loss of energy. This means that the final speeds of the protons will depend on their masses and initial speeds, and it is possible for them to end up with the same speed.

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