## Questions like the HSC 2020 exam

Due to copyright the actual exam questions can not be published here.

Please refer to the 2020 HSC Physics exam for the published questions.

## like question 17

A spacecraft passes you travelling at 0.866c to the right. There are two mirrors A and B separated by 10 metres. A photon is travelling inside the spacecraft from mirror A to mirror B.

Which of the following statements is true?

- The photon has a velocity of 0.134c relative to you.
- You measure the photon as travelling a greater distance than 10 metres.
- You see the photon take a shorter time than 10/c.
- You measure the photon as travelling 10 metres.

In the above animation observe the photons moving in the opposite direction to the spacecraft, and compare it to the stationary spacecraft.

Once again observer the photon moving in the opposite direction to the spacecraft. Compare the time it takes to exit the grid when stationary and when the spacecraft is moving at 0.866c.

## like question 22

A spacecraft is in orbit about Earth travelling at 8 400 m/s relative to a tracking station on Earth. It fires its main rocket to propel it to Mars and reaches a speed of 32 000 m/s. The rocket engine expelled the gas at 4 300m/s.

Outline TWO limitations of applying special relativity to the analysis of the motion of the capsule.

Marking Guide Answer

The speed of the spacecraft is not a significant fraction of the speed of light, hence the effects of special relativity are insignificant. The capsule is in a non-inertial frame because it is accelerating, and therefore special relativity is not applicable.

This limits applying special relativity to the motion of the capsule.

The first axiom of relativity states that all uniform motion is relative. The theory does not incorporate acceleration. Though in the above problem you could use relativity to work out the change in energy of the capsule if you knew its mass. However the classical expression for kinetic energy, expressed as ½mv^{2}, would be sufficiently accurate given the number of significant figures of the initial values.

At 32 000 m s^{–1} this speed is 0.000106c. This velocity is too small a value to type input into the animated graph. At this speed the relativistic time dilation is 0.9999999943, indicating the relativistic effect is extremely small and has no practical advantage over using more classical physics.

## like question 30

(b) (i) Calculate the wavelength of a neutron travelling at 0.05c .

Marking Guide Answer

### λ= h/mv

### λ= 6.626x10^{-34}/(1.67493x10^{-27}x0.05x3x10^{8})

### λ= 2.63x10^{-14} m

(ii) Explain how the relativistic momentum of a neutron travelling at 0.99c compares to the Newtonian momentum. What effect would this have on the calculated wavelength of the neutron.

Marking Guide Answer

The relativistic momentum is greater than would be predicted by classical mechanics, and so the relativistic wavelength is shorter than the classical.