An electron and a proton are each accelerated through a potential difference of 10.0 million volts.

a) What is the kinetic energy of the electron? What is the kinetic energy of the proton?
b) Calculate the momentum (MeV/c) of the proton using classical equations.
c) Calculate the momentum (MeV/c) of the proton using relativistic equations.
d) Calculate the momentum (MeV/c) of the electron using classical equations.
e) Calculate the momentum (MeV/c) of the electron using relativistic equations.
f) Why is there a difference?

Solution Preview

a) The kinetic energies of both the proton and the electron are 10.0 MeV since they each have a charge of +/-e.

b) The classical momentum P_c of the proton is given by

Using the relativistic expression for total energy E and the magnitude p of the momentum of a particle
a) Show that the two quantities are related by E^2=(p^2)(c^2)+[m(c^2)]^2
b) Use this expression to determine the linear momentum of a proton with a kineticenergy of 1000MeV.

1. State the conservation of momentumandkineticenergy in collisions in classical mechanics andrelativistic mechanics
2. derive the relativistickineticenergy.
3. Derive the total relativistic force as a function of momentum.
please show the solutions in detail, stepwise.

Prove that the De Broglie wavelength associated with a particle having kineticenergy 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.

(a) Show that the kineticenergy of a nonrelativistic particle can be written in terms of its momentum as KE = P2 (squared)/2m. (b) Use the results of (a) to find the minimum kineticenergy of a proton confined within a nucleus having a diameter of 1.0 x 10-15 m.

Using the classical andrelativistic expressions for kineticenergy, calculate the range of velocities for a particle of mass m such that we use the classical expression for kineticenergy to within an accuracy of 1%.

9-The Tevatron accelerator at the Fermi National Accelerator Laboratory (Fermilab) outside Chicago actually consists of 5 stages to sequentially boost protons to 1 TeV (1000 GeV). What is the speed of the proton at the end of each stage? Note: the numbers given in parentheses represent the total kineticenergy at the end of each

The operator of a linear particle accelerator tells a tour group that it is used to give protons an energy of 600MeV.
a) this 600MeV must refer to the protons total, kinetic, or rest energy? Why?
b) what are the values of these three proton energies?
c) what is the protons speed?
d) what is the protons moment

A football player with a mass of 88 kg and a speed of 2.0 m/s collides head-on with a player from the opposing team whose mass is 120 kg. The players stick together and are at rest after the collision. Find the speed of the second player, assuming the speed of light is 3.0 m/s.

A 0.4kg ball moving with speed of 3m/sec collides with a 0.6kg mass initially at rest. If the two particles stick together during the collision, find the momentum, velocity, andkineticenergy of the system after the collision.