Special Relativity (AQA A Level Physics)

A student models a spacecraft journey that takes one year. The spacecraft travels directly away from an observer at a speed of 1.2 × 10⁷ m s⁻¹ . The student predicts that a clock stationary relative to the observer will record a time several days longer than an identical clock on the spacecraft.

Comment on the student’s prediction. Support your answer with a time dilation calculation.

In practice, the gravitational field of the Sun affects the motion of the spacecraft and it does not travel directly away from the Earth throughout the journey.

Explain why this means that the theory of special relativity cannot be applied to the journey.

Cosmic rays detected on a spacecraft are protons with a total energy of 3.7 × 10⁹ eV.

Calculate the velocity of the protons as a fraction of the speed of light.

Table 1 shows data of speed and kinetic energy for electrons from a modern version of the Bertozzi experiment.

Table 1

Classical mechanics predicts that .

Deduce whether the data in Table 1 are consistent with this prediction.

Discuss how Einstein’s theory of special relativity explains the data in Table 1.

Calculate, in J, the kinetic energy of one electron travelling at a speed of 0.95c.

Einstein developed his theory of special relativity from two postulates. One postulate states that physical laws have the same form in all inertial frames.

State the other postulate and explain how it is consistent with the equation:

A proton leaves a particle accelerator at point X and moves at a constant speed towards a target at point Y. The speed of the proton is 2.5 × 10⁸ m s⁻¹ in the frame of reference of the target.

The distance XY in the frame of reference of the proton is 38 m.

Calculate the distance XY in the frame of reference of the target.

Give your answer in metres.

Show that the kinetic energy of the proton is about 1.2 × 10⁻¹⁰ J.

Sketch on Figure 4 the variation of with speed for a proton.

To help you, the dashed line represents

where is equal to the mass of a proton at rest.

Figure 4