Question

at what velocity in respect to c does the relativistic kinetic energy differ from the classical kinetic energy by? (a)1% (b)10% (c) 50% ? PLEASE SHOW ALL WORK

Answer 1

K.F = 1/2, mv^2 we know mass of object in motion m = m_0/squareroot 1 - v^2/c^2 so for 1% difference m = 1.01m_0 1.01m_0 = m_0/squareroot 1 - v^2/c^2 1 - v^2/c^2 = (1/1.01)^2 = 0.98029 v^2/c^2 = 0.0197 v^2 = 0.0197 times (3 times 10^8)^2 v = 4.2 times 10^- 7 m_0^- 1 For 10% increases m = 1.1m_0 so 1.1m_0 = m_0/squareroot 1 - v^2/c^2 so 1 - v^2/c^2 = (1/1.1)^2 1 - v^2/c^2 = 0.8264 v^2/c^2 = 0.1735 v = 1.249 times 10^8 ms^- 1 For 50% increases m = 1.5m_0 1.5m_0 = m_0/squareroot 1 - v^2/c^2 1 - v^2/c^2 = 1/(1.5)^2 1 - v^2/c^2 = 0.4444 so v = 2.236 times 10^8 ms^- 1