Particles accelerators such as the Large Hadron Collider (LHC) can accelerate particles up to tremendous energies. Suppose the LHC accelerates alpha particles (a.k.a. helium nuclei with a charge of +2e and a mass of 6.645 x 1027 kg) with a kinetic energy of 7.5 TeV*, what would the speed of one particle be if relativistic effects** are ignored? Give your answer in units of Gm/s. *T as in Tera, for 1012. "eV" stands for "electron volt," which is a non-Sl unit of energy equal to what one electron would gain after travelling through 1V. 1eV = 1.602 x 1019 J. **Special relativity is necessary to correctly account for the limiting speed of light, which is about 3 x 10° m/s. Note that in ignoring this effect and applying Newtonian mechanics (what you learned in Phys1210 or equivalent), you'll be getting a speed way above 0.3 Gm/s. That's just how insanely energetic the LHC is.

Derive 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.

Modern physics

measured by this observer to be 10 times longer than its lifetime when at rest relative to the observer? 3. The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.9 x 108m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? 4. A computer in a laboratory requires 2.50 us to make a certain calcu- lation, as measured by a scientist in the lab. To someone moving past the lab at a relative speed of 0.995c, how long will the same cal- culation take? 5. The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as V1-v²/c² times the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 95 percent the speed of light? 6. If an electron is speeding down the two-mile-long Stanford Linear Accelerator at 99.98 percent the speed of light,…