## Sunday, January 30, 2011

### Mastering Physics: ± Creating a Particle

Two protons (each with rest mass ) are initially moving with equal speeds in opposite directions. The protons continue to exist after a collision that produces an particle. The rest mass of the is .

Part A
If the two protons and the are all at rest after the collision, find the initial speed of the protons.
Express your answer as a fraction of the speed of light to three significant figures. = 0.6331 Part B What is the kinetic energy of each proton?
Express your answer in millions of electron volts to three significant figures. = 273.7 Part C What is the rest energy of the ?
Express your answer in millions of electron volts to three significant figures. = 547.3 Notice that the rest energy of the is equal to the total kinetic energy of the two protons, as expected from the conservation of energy.

### Mastering Physics: Work Required to Accelerate Relativistic Particles

Part A
How much work must be done on a particle with a mass of to accelerate it from rest to a speed of 0.909 ?
Express your answer as a multiple of to three significant figures. = 1.399 Part B How much work must be done on a particle with a mass of to accelerate it from a speed of 0.909 to a speed of 0.990 ?
Express your answer as a multiple of to three significant figures. = 4.69 ### Mastering Physics: Relativistic Energy and Momentum

Learning Goal: To learn to calculate energy and momentum for relativistic particles and, from the relativistic equations, to find relations between a particle's energy and its momentum through its mass.
The relativistic momentum and energy of a particle with mass moving with velocity are given by and Part A
Find the momentum , in the laboratory frame of reference, of a proton moving with a speed of 0.899 . Use for the mass of a proton.
Express your answer in to three significant figures. = 1925 Part B
Find the total energy of this proton in the laboratory frame.
Express your answer in millions of electron volts to three significant figures. = 2142 Part C
What is the value of the expression for this proton?
Express your answer in millions of electron volts squared to three significant figures. = 8.80×105 The answer to this part is numerically equal to the rest mass of the proton squared. In fact, this result points to a very important equation in relativistic physics: . This formula indicates an equivalence between mass and energy, which was first realized by Albert Einstein.
Part D What is the rest mass of a particle traveling with the speed of light in the laboratory frame.
Express your answer in to one decimal place. = 0 