In the first upgrade of the Large Hadron Collider, each of the colliding proton beams was designed to reach an energy of 7 TeV (7 × 10'2 eV). What is the corresponding Lorentz y -factor and what is u/c for a proton beam of this energy, given that in special relativity the total energy E is given by E = ymc2, where m is the rest mass?
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- The mass of a proton is 1.67 × 10-27 kg. Part (a) Find the rest energy in joules. Part (b) Find the rest energy in mega-electron volts.Suppose that you have found a way to convert the rest energy of any type of matter directly to usable energy with an efficiency of 57.0%. How many liters of water would be sufficient fuel to very slowly push the Moon 1.50 mm away from the Earth? The density of water is Pwater = 1.00kg/liter, the Earth's mass is Mearth 5.97 x 1024 kg, the Moon's mass is М, = 7.36 x 1022 kg, and the separation of the Earth and Moon is de.M 3.84 x 10° m. moon water: LitersPlease type instead of hand writting
- Suppose that you have found a way to convert the rest energy of any type of matter directly to usable energy with an efficiency of 85.0%. How many liters of water would be sufficient fuel to very slowly push the Moon 2.90 mm away from the Earth? The density of water is pwater = 1.00kg/liter, the Earth's mass is Mearth = 5.97 x 1024 kg, the Moon's mass is Mmoon = 7.36 x 10²² kg, and the separation of the Earth and Moon is deM = 3.84 × 10% m. water: LitersDerive an expression for E using the attached equation (Lorentz Force Law), and calculate a predicted value for E in N/C if a particle had v = 40 m/s, q = -0.001 C, m = 0.3 ⨉ 10 -3 kg, and B = 0.6 T.The Tevatron was a large particle accelerator that would collide beams ofprotons and anti-protons to see what would come out of the collisions.a) Let’s assume that each particle (in both beams) was accelerated to a total energy of100 GeV. What is the speed of the protons (relative to the speed of light) if you assumethe mass of the proton is equal to 1 GeV/c^2? Write your answer in terms of the speed oflight—keep it as a decimal times “c”. You will need several decimal places.b) Suppose that you now accelerate each particle to a speed of 0.9c. Since they are movingin opposite directions, what is the speed that one would measure for the speed of the otherparticle? Just give the absolute value of this speed. Don’t worry about the sign.c) Given your answer in part b, what is the energy of that one particle would measure forthe other particle?
- If ever the human race would need to leave Earth, the Trappist-1 system might make a good destination – the star there has seven temperate terrestrial planets, a few of which are close to Earth’s size and mass. It’s 39.6 light years away, though, so it could take a long time to get there. (a) If the spaceship had a speed of 0.95c, how long would the journey take from the Earth’s reference frame? (b) How long would the journey be for the passengers on the spaceship?The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 10-8 s. (a) If the meson moves with a speed of 0.94c, what is its mean lifetime as measured by an observer on Earth? (b) What is the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur?Albert Einstein’s theory of relativity, which he developed in the context of his special theory of relativity, are inconsistent with several experiments. This is not the case with the general theory of relativity, whose predictions coincide with the experiments without contradiction and whose experimental confirmations were celebrated as great scientific achievements. The latter made the physicists obviously blind to the contradictions of the foundations of the theory of relativity and led to an immunization against critical statements on the theory of relativity. Explain this in simpler terms.
- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)A particle's dynamics are considered "relativistic" when its velocity is a significant fraction of the speed of light. For example, the mass of a moving particle seen by a stationary observer increases in proportion to the square root of 1/(1 - (v/c)2). For typical speeds in the everyday world it is not noticeable, but take a fast moving fundamental particle and you may have apparent mass increases or changes in its lifetime as a consequence of time dilation. Look at this factor for the electron you measured at 100 V in the glass globe. Pick the best answer. The effect is less than 0.1 %. The effect is around 1%. The effect is around 10%. The effect is a factor of 2 change in mass.A car is moving relative to a pedestrian with a Lorentz factor of 1.45. With the length of the car being 5.7m according to the pedestrian, what's the length according to the driver of the car (he's moving at the same speed of the car) ?