Proton Collision Experiment: Calculating Second Proton Velocity

What is the velocity (magnitude and direction) of the second proton after the collision?

Given initial and final velocities of the first proton after a collision in an experiment, how can we calculate the final velocity of the second proton? What are the steps and equations involved in this calculation?

Answer

The velocity of the second proton after the collision is 14,435.02 m/s at an angle of approximately 60° with respect to the x-axis.

In a lab experiment, a proton is shot directly to the right at 50,000 m/s towards another proton. After the collision, the first proton moves at an angle of 30° with respect to the +x axis at a speed of 43,300 m/s. This scenario involves an elastic collision between two protons, where linear momentum and energy are conserved.

To calculate the velocity of the second proton after the collision, we need to consider the conservation of linear momentum and energy. By analyzing the x and y components of linear momentum before and after the collision, we can set up equations to solve for the final velocity of the second proton.

After applying the conservation equations and solving for the final velocity of the second proton, we find that the magnitude of its velocity is 14,435.02 m/s. The direction of this velocity is approximately 60° with respect to the x-axis.

By understanding the principles of conservation of linear momentum and energy in elastic collisions, we can accurately determine the final velocity of particles involved in such experiments. The calculation process involves careful consideration of the initial and final conditions of the system, as well as the equations derived from these conditions.