3 The relativistic addition of velocities Let us now modify our timing device, as shown in Fig20-7 The flashing bulb F is moved to the mirror end and is replaced by a device P that emits particles at a speed vo,as measured by an observer at rest with respect to the device → particle P light
3 The relativistic addition of velocities Let us now modify our timing device, as shown in Fig20-7. The flashing bulb F is moved to the mirror end and is replaced by a device P that emits particles at a speed , as measured by an observer at rest with respect to the device. light P D F particle 0 v L0 → v0
The time interval Ato measured by an observer(such as s) who is at rest with respect to the device is (20-9) 0 What's the velocity of the particles, measured by the observer s on the ground? O voll (20-12) Eg(20-12) gives one form of the velocity addition law
The time interval measured by an observer (such as S’) who is at rest with respect to the device is: (20-9) 0 t C L v L t 0 0 0 0 = + What’s the velocity of the particles, measured by the observer S on the ground? 2 0 0 1 c v u v u v + + = (20-12) Eq(20-12) gives one form of the velocity addition law
(a According to Galileo and Newton, a projectile fired forward at speed vo in a train that is moving at speed u should have a speed vo +u relative to an observer on the ground This clearly permits speeds in excess of c to be realized
(a) According to Galileo and Newton, a projectile fired forward at speed in a train that is moving at speed u should have a speed relative to an observer on the ground. This clearly permits speeds in excess of c to be realized. 0 v v + u 0
(b) The Eg(20-12) prevents the relative speed from ever exceeding c Vo +u (a)If vo <<c ≈V0+l 1+2 (b)If C+u C C cu 1+2 Thus, Eq (20-12) is consistent with Einstein,'s second postulate
(b) The Eq(20-12) prevents the relative speed from ever exceeding c. (a)If (b)If Thus, Eq(20-12) is consistent with Einstein’s second postulate v c 0 v u c v u v u v + + + = 0 2 0 0 1 v = c 0 c c cu c u v = + + = 2 1
Sample problem 20-2 A spaceship is moving away from the earth at a speed of 0.80c when it fires a missile parallel to the direction of motion of the ship. The missile moves at a peed of 0.60c relative to the ship. What would be the speed of the missile as measured by an observer on the earth? Compare with the predictions of Galilean kinematics
A spaceship is moving away from the Earth at a speed of 0.80c when it fires a missile parallel to the direction of motion of the ship. The missile moves at a peed of 0.60c relative to the ship. What would be the speed of the missile as measured by an observer on the Earth? Compare with the predictions of Galilean kinematics. Sample Problem 20-2