**Collision of Protons in a Particle Accelerator****Situation Overview:**A proton is accelerated in a particle accelerator and undergoes an elastic collision with a stationary proton in a cooled hydrogen target.**Given Data:**- Mass of both protons \( m_1 = m_2 = 1.672 \times 10^{-27} \, \text{kg} \)- Initial velocity of the moving proton \( v_{1i} = 8.2 \times 10^5 \, \text{m/s} \)- Initial velocity of the stationary proton \( v_{2i} = 0 \, \text{m/s} \)- Angles of deflection after collision: - \( \theta_1 = 30^\circ \) - \( \theta_2 = 60^\circ \)**Illustration Overview:**The diagram shows the initial and final velocities and angles of the protons after the collision. The system uses a standard x-y axis for reference.**Tasks:**a.) **Write out the conservation equations for this collision geometry.**b.) **Solve for the velocities of the two protons after the collision**: - \( v_{1f} \) - \( v_{2f} \)c.) **Compute the velocity of the center of mass.**This scenario involves applying principles of conservation of momentum and, since it's an elastic collision, conservation of kinetic energy as well.

E m1 Vii m₂ 8₁ v2f 4. A proton is accelerated in a particle accelerator and collides elastically with a stationary proton in a cooled hydrogen target. m₁ = m₂ = 1.672 x 10-27 V₁i = 8.2 x 105 m/s 0₁ = 30° 0₂ = 60° kg V₂i = 0 m/s a.) Write out the conservation equations for this collision geometry. b.) Solve for the velocities of the two protons after the collision: v₁f and v₂f. c.) Compute the velocity of the center of mass.

E m1 Vii m₂ 8₁ v2f 4. A proton is accelerated in a particle accelerator and collides elastically with a stationary proton in a cooled hydrogen target. m₁ = m₂ = 1.672 x 10-27 V₁i = 8.2 x 105 m/s 0₁ = 30° 0₂ = 60° kg V₂i = 0 m/s a.) Write out the conservation equations for this collision geometry. b.) Solve for the velocities of the two protons after the collision: v₁f and v₂f. c.) Compute the velocity of the center of mass.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

**Collision of Protons in a Particle Accelerator**

**Situation Overview:**
A proton is accelerated in a particle accelerator and undergoes an elastic collision with a stationary proton in a cooled hydrogen target.

**Given Data:**
- Mass of both protons \( m_1 = m_2 = 1.672 \times 10^{-27} \, \text{kg} \)
- Initial velocity of the moving proton \( v_{1i} = 8.2 \times 10^5 \, \text{m/s} \)
- Initial velocity of the stationary proton \( v_{2i} = 0 \, \text{m/s} \)
- Angles of deflection after collision:
- \( \theta_1 = 30^\circ \)
- \( \theta_2 = 60^\circ \)

**Illustration Overview:**
The diagram shows the initial and final velocities and angles of the protons after the collision. The system uses a standard x-y axis for reference.

**Tasks:**

a.) **Write out the conservation equations for this collision geometry.**

b.) **Solve for the velocities of the two protons after the collision**:
- \( v_{1f} \)
- \( v_{2f} \)

c.) **Compute the velocity of the center of mass.**

This scenario involves applying principles of conservation of momentum and, since it's an elastic collision, conservation of kinetic energy as well.

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