Table 1 shows experimental data for the speed vvv and kinetic energy EkE_kEk of protons accelerated in a relativistic synchrotron.
Table 1
| v/108 m s−1v / 10^{8}\text{ m s}^{-1}v/108 m s−1 | Ek/GeVE_k / \text{GeV}Ek/GeV |
|---|---|
| 1.501.501.50 | 0.140.140.14 |
| 2.102.102.10 | 0.380.380.38 |
| 2.402.402.40 | 0.630.630.63 |
| 2.702.702.70 | 1.211.211.21 |
| 2.852.852.85 | 2.072.072.07 |
Newtonian (classical) mechanics predicts that kinetic energy is directly proportional to the square of the speed, Ek∝v2E_k \propto v^2Ek∝v2.
Deduce whether the data in Table 1 support this Newtonian prediction.
Explain how Einstein's theory of special relativity accounts for the relationship between speed and kinetic energy shown by the data in Table 1.
Calculate, in J, the kinetic energy of a proton travelling at a speed of 0.85c0.85c0.85c.
(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.)
