An electrostatic linear accelerator (LINAC) is used to study the relativistic properties of high-speed protons. A pulsed beam of protons is accelerated from rest through a total potential difference (pd) of 480 MV480 \text{ MV}480 MV and directed towards a graphite block detector.
Show that each proton gains approximately 7.7×10−11 J7.7 \times 10^{-11} \text{ J}7.7×10−11 J of kinetic energy.
The pulse of protons causes the temperature of a 1.20 kg1.20 \text{ kg}1.20 kg graphite block to increase by 4.06 K4.06 \text{ K}4.06 K. The total number of protons in the pulse is 4.50×10134.50 \times 10^{13}4.50×1013.
Deduce whether this observed temperature increase is consistent with an accelerating pd of 480 MV480 \text{ MV}480 MV.
The speed of the protons between the accelerator's final stage and the detector block is measured to be 2.25×108 m s−12.25 \times 10^8 \text{ m s}^{-1}2.25×108 m s−1.
Evaluate both suggestions using calculations of the kinetic energy of a proton at this speed.
A laboratory timer records the time taken for the proton pulse to travel from the final collimator to the graphite block as 12.0 ns12.0 \text{ ns}12.0 ns.
What is the proper time interval for a proton travelling this distance?
The protons were accelerated from rest in 161616 stages, each using a pd of 30 MV30 \text{ MV}30 MV.
Compare, for a proton:
Justify your answer. No further calculations are required.
