The LHC accelerates protons to a speed of 0.999999991c around a 27km ring. Due to relativistic effects, their mass increases. Given that the magnetic fields used are 8T, calculate this mass. What is the total energy of an LHC beam containing 3e14 protons?
Balancing the centripetal force mv^2/r with the force experienced due to motion in a magnetic field qvB: m = qBr/v = qBC/2piv (C circumference). Putting in numbers: m = 1.83e-23 kg (~11,000 mass of proton at rest!). Energy of beam = Np * 1/2 m v^2 (Np number of protons). Again, using the numbers, we get energy = 2.4e8 J. This is equivalent to the energy a standard car (mass 1.5t) has when traveling at around 1300 mph! (I originally asked this in the question but I went over the character count!).
TD
Related Physics A Level answers
All answers ▸A projectile is launched from ground level with a speed of 25 m/s at an angle of 42° to the horizontal. What is the horizontal distance from the starting point of the projectile when it hits the ground?
The electric potential energy of two protons is 1.0MeV. Calculate their separation
An ideal gas at a temperature of 22 C is trapped in a metal cylinder of volume 0.2 m^3 at a pressure of 1.6x10^6 Pa. The gas has a molar mass of 4.3 x 10^(-2) kg mol^(-1). Calculate the density of the gas in the cylinder.
Single electrons travelling at 550 ms^-1 are passed through a diffraction grating with a spacing between the slits of 2.5 micrometers. What would the angle between the zeroth and first maximum of the resulting interference pattern be?