Question

For each questions, please show me all your work and explain the answer.

1. A rocket is moving at 1/4 c relative to Earth. At the center of this rocket, a light source suddenly flashes. To an observer at rest in the rocket

a. the light pulse will reach the front of the rocket at the same instant that it reaches the back of the rocket.

b. the light pulse will reach the front of the rocket before it reaches the back of the rocket.

c. the light pulse will reach the front of the rocket after it reaches the back of the rocket.

2. A rocket is moving at 1/4 c relative to Earth. At the center of this rocket, a light source suddenly flashes. To an observer at rest on Earth

a. the light pulse will reach the front of the rocket at the same instant that it reaches the back of the rocket.

b. the light pulse will reach the front of the rocket before it reaches the back of the rocket.

c. the light pulse will reach the front of the rocket after it reaches the back of the rocket.

3. An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats. What will observers in all other inertial reference frames measure for the time interval between her heartbeats?

a. more than Δt

b. Δt

c. less than Δt

d. The answer depends on whether they are moving toward her or away from her.

4. The special theory of relativity predicts that there is an upper limit to the speed of a particle. It therefore follows that there is also an upper limit on the following properties of a particle.

a. the kinetic energy

b. the total energy

c. the linear momentum

d. more than one of these

e. none of these

5. In a linear collider, two particles travel toward each other from opposite directions before colliding. If, in the lab reference frame, an electron travels toward the collision point at 2/3 c and a positron travels at 3/4 c, at what speed does the electron travel toward the positron in the positron’s reference frame? (Be sure to show all of the steps of your calculation without using a calculator.)

Answer 1

1. Rocket is moving relative to Earth at a speed of 1/4 c and the light source is at the center of the rocket. Here, the observer is at rest as he is sitting inside the rocket so between the observer and the rocket there is no relative motion so the light flash will take the same amount of time to reach the back and the front of the rocket as the source is situated at the center of the rocket.

Hence, option(a) the light pulse will reach the front of the rocket at the same instant that it reaches the back of the rocket. is correct.

2) Now the observer is sitting on Earth and hence there is a relative motion taking place so if tp is the proper time measured in the above case so here, the measured time tp' will come out to be

The above amount of time will be taken by the pulse to reach in front and in back so again in this scenario option (a) is correct although the time measurements will be different in two cases but the light flashes will take the same amount of time to reach the front and the back of the rocket. HEnce option (a)

the light pulse will reach the front of the rocket at the same instant that it reaches the back of the rocket. is valid .

Please post all other questions separately