Table 1 shows data of speed vvv and kinetic energy EkE_kEk for protons accelerated in a relativistic particle facility.
Table 1
| v/108 m s−1v / 10^{8}\text{ m s}^{-1}v/108 m s−1 | Ek/MeVE_k / \text{MeV}Ek/MeV |
|---|---|
| 1.201.201.20 | 858585 |
| 1.801.801.80 | 235235235 |
| 2.402.402.40 | 626626626 |
| 2.702.702.70 | 121412141214 |
| 2.912.912.91 | 292129212921 |
Classical mechanics predicts that Ek∝v2E_k \propto v^2Ek∝v2.
Deduce whether the data in Table 1 are consistent with this prediction.
Discuss how Einstein's theory of special relativity explains the trends observed in Table 1.
Calculate, in J, the relativistic kinetic energy of a proton travelling at a speed of 0.88c0.88c0.88c.
(Take the rest mass of a proton as mp=1.67×10−27 kgm_p = 1.67 \times 10^{-27}\text{ kg}mp=1.67×10−27 kg and the speed of light in a vacuum as c=3.00×108 m s−1c = 3.00 \times 10^8\text{ m s}^{-1}c=3.00×108 m s−1.)
