You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an approximated density of 1 hydrogen atom/m3 . (a) Calculate the time it takes your spaceship to reach Sirius. (b) Determine the mass of interstellar gas that collides with your spaceship during the mission. Note: Use 1.673 × 10−27 kg as proton mass. Considering the effect of time dilation c)how many years will have passed from your perspective?d) at what earth date will you arrive to earth? ( your spaceship launches in june 2020 and returns back to earth directly from sirius)

A particle has γ=18,399. a)Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, 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 1,739 MeV/c, calculate its energy in MeV.

dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.

Helpful information: (1) An alpha particle is a helium nucleus, (2) e = 1.6 × 10-¹⁹ C, (3) k₂ = 9.0 × 10⁹ Nm² C-2, (4) 1nm = 1 × 10-⁹ m 1-An alpha particle lies on the x-axis, a distance of 1.0 nanometer from a proton (in this set-up, the alpha particle is at the origin while the proton is in the positive direction). Which of the following choices below represents the magnitude of the electric force on the alpha particle? (a) 2.3 × 10-10 N (b) 4.6 × 10-10 N (c) 2.3 x 10-19 N (d) 4.6 x 10-19 N cing the voltage so following insta choices below at a time! 1.00 s?