Collision of charged particles}} A proton moves in vacuum and enters a region where there's another proton at rest. The protons interact and the angle between their velocities is measured when they are far away from each other. What is the most likely value for this angle in degrees ?
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- Calvin Lin
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To determine the most likely value for the angle between the velocities of the protons, we can consider the principles of conservation of momentum and conservation of energy.
When the proton initially at rest interacts with the moving proton, both momentum and energy are conserved in the system. The sum of the momenta before the collision is equal to the sum of the momenta after the collision, and the total energy before the collision is equal to the total energy after the collision.
Assuming an elastic collision (no energy loss or deformation), the final velocities of the protons after the collision can be obtained using the following equations:
Momentum Conservation:
m1 * v1i = m1 * v1f + m2 * v2f
Energy Conservation:
1/2 * m1 * v1i^2 = 1/2 * m1 * v1f^2 + 1/2 * m2 * v2f^2
Where:
m1 and m2 are the masses of the protons (which are equal since they are both protons) and can be assumed to be approximately 1.67 × 10^(-27) kg.
v1i and v2i are the initial velocities of the moving and resting protons (which can be given or calculated using known values such as kinetic energy), respectively.
v1f and v2f are the final velocities of the moving and resting protons after the collision.
Using these equations, we can find the final velocities of the protons. From there, we can calculate the angle between their velocities by using the vector dot product or by using trigonometric relationships.
Keep in mind that the actual value of the angle between the velocities can vary depending on the initial conditions and other factors. However, the most likely value for the angle between their velocities in this specific scenario is zero degrees (collinear motion) since both protons have the same mass and are not subject to external forces.