How many years would you have to wait to observe a 18 angular shift in the perihelion of Mercury due to general relativistic effects?

The carbon isotope 14C is used for carbon dating of objects.  A  14C nucleus can change into a different kind of element, a neighbor on the periodic table with lower mass, by emitting a beta particle – an electron or positron – plus a neutrino or an anti-neutrino.  Consider the scenario where 14C ( mass of 2.34 x 10 -26) decays by emitting an electron and anti neutrino.  The electron has a mass of 9.11x 10-31 kg and a speed of 5.5 x107  m/s.  While the anti neutrino has  a momentum of 8.5x10-24 kg-m/s.  If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.

At the Fermilab accelerator, protons of momentum 5.3 × 10-16 kg.m/s are held in a circular orbit of diameter 2 km by a vertial B. Find the magnitude of the B required for this task.

A particle has γ=9,681 (has a decimal point) Gamma is chosen to make the particle extremely close to the speed of light. In a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle.  We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light.  ("Massless particles" -- gamma and m have to be eliminated from the expressions.  Light is a true massless particle.) If a massless particle has momentum 1,368 MeV/c, calculate its energy in MeV.

Quasars are thought to be the nuclei of active galaxies in the early stages of their formation. A typical quasar radiates energy at the rate of 1041 W. At what rate is the mass of this quasar being reduced to supply this energy? Express your answer in solar mass units per year, where one solar mass unit (1 smu = 2.0*10^30 kg) is the mass of our Sun.

A futuristic rocket ship of mass m,hip = 6.0 × 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant. (d) When at the final speed of 0.95c, by what factor is the ship's…

Osmium (the densest metal found on the periodic table) has a mass density, ρo = 22,500 kg/m3 when it's sitting still.If a sample of osmium is moving with enough speed that its kinetic energy is equal to one-quarter its own rest energy, what is its mass density, ρ', as measured by a stationary observer? (Remember ρ' = m' / V' ) Group of answer choices ρ' = (5/4) ρo ρ' = (25/16) ρo ρ' = (9/25) ρo ρ' = ρo ρ' = (3/5) ρo

Imagine that the entire Sun collapses to a sphere of radius R g such that the work required to remove a small mass m from the surface would be equal to its rest energy mc 2. This radius is called the gravitational radius for the Sun. Find R g . (It is believed that the ultimate fate of very massive stars is to collapse beyond their gravitational radii into black holes.)

Two neutron stars are separated by a distance of 1.0 x 1011 m. They each have a mass of 1.0x 1031 kg and a radius of 1.0 x 107 m. They are initially at rest with respect to each other. As measured from that rest frame, how fast are they moving when (a) their separation has decreased to one-half its initial value and (b) they are about to collide? (a) Number i Units (b) Number i Units