Relativity: Conservation of momentum particle question

1. Conservation of Momentum and COM reference frame: Two particles are sliding directly towards each other on a frictionless surface. According to an observer in the laboratory reference frame, a 3.00kg particle moves to the right at 10.00m/s and a 5.00kg particle moves towards the left at 2.00m/s. After the head-on collision, the particles stick together ...

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(a) Velocity of the CM lab reference frame
= (towards right)

(b) Momentum of particle of mass 3 kg w.r.t. CM frame = 3*(10-2.5)
= 22.5 kg-m/s (towards right)
Momentum of particle of mass 5 kg w.r.t. CM frame = 5*(-2 - 2.5) = -22.5 kg-m/s
or 22.5 kg-m/s (towards left)

(c) Total momentum = Total momentum of two particles in the Center of Mass reference frame = 22.5 -22.5 = 0

(d) Velocity of the combined mass in lab reference frame
= (towards right)

(a) t = distance/ speed = (65/0.8c) second = ...

Solution Summary

The conservation of momentum particle relativity is examined. A head-on collision of particles are analyzed.

A particle of mass 3.5 MeV/c2 and kinetic energy 4.5 MeV collides with a stationary particle of mass 0.5 MeV/c2 . After the collision, the particles stick together.
(part 1 of 5)
Find the total energy of the first particle before the collision. Answer in units of MeV.
(part 2 of 5)
Find the speed of the first particl

A particle of mass m and velocity Vo collides elastically with a particle of mass M initially at rest and is scattered through angle, A, in the center of mass system.
a) Find the final velocity of m in the laboratory system.
b) Find the fractional loss of kinetic energy of m.

This solution shows how to develop the algebra to determine the velocity of a nuclear particle fragment resulting from the fragmention of a nuclear particle into two fragments. An example is shown whereby a particle initially at rest fragments into two fragments one of mass (m1) = 1.67 x E-27 Kg. and velocity of (v1) = 0.8c, the

An electron moving in the positive x-direction is characterized by GAMMA = 1000 and BETA = 1 - 5 x 10^-7 which for this problem you can take as 1. A photon of energy hν, traveling at 45 degrees with respect to the x axis collides with the electron. The collision results in the creation of an electron-positron pair plus an

Part 1
The speed of light is 2.998 * 10 ^8 m/s. Find the ratio of the total energy to the rest energy of a particle of rest mass m0 moving
with speed 0.26 c.
Part 2
The K^0 particle has a mass of 497.7 MeV/c^2 . It decays into aPi- and Pi+, each with mass 139.6 MeV/c2 . Following the decay of a K^ 0, one of the pions is

Prove that the De Broglie wavelength associated with a particle having kinetic energy K which is not negligible compared to its rest energy m_0 c^2 is given by
lemda = [h/(m_0 K)^(1/2)](1 + K/2m_0 c^2)^(-1/2)
The complete solution is in the attached file.

An instrument carrying projectile accidentally explodes at the top of its trajectory. The horizontal distance between the launch point and the point of explosion is L. The projectile breaks into pieces which fly apart horizonally. The larger piece has three times the mass of the smaller piece. To the surprise of the scientist in

At t=0, the wavefunction of a free particle is:
psi(x,0) = {(sqrt b/2*pi)sin(bx) for |x|<((2*pi)/b)
{0 for |x|> or = ((2*pi)/b))
a) What is the probability of finding the particle in the interval 0 less than or equal to x less than or equal to pi/2b?
b) What is the momentum am

Two particles each have a mass of 5.4 x 10-2 kg. One has a charge of +4.8 x 10-6 C, and the other has a charge of -4.8 x 10-6 C. They are initially held at rest at a distance of 1.1 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its