Relativistic momentum & paradoxes

A particular task requires 20.0 J of energy. How much mass is equivalent to this amount of energy?

•  $20.0\times\left(3.0\times10^8\right)\ kg$ 
  

•  $\frac{20.0}{\left(3\times10^8\right)^{2\ }}kg$ 

•  $\frac{20.0}{3\times10^8\ }kg$ 

•  $\frac{\left(3\times10^8\right)^2}{20.0}kg$ 

At what speed will an electron’s relativistic momentum be exactly 1.5 times its Newtonian momentum?

• 0.5c

• 0.87c

• 0.75c

• 0.6c

What is the relativistic momentum of an object with a rest mass of 1.0 kg travelling at 0.85c?

• 1.6 kgm/s

• 0.85 kgm/s

• 0.45 kgm/s

• 100 kgm/s

Which one of the following is a true statement about momentum?

• Newtonian momentum remains constant as speed is increased.

• Relativistic momentum doubles when speed is doubled.

• At low speeds Newtonian momentum is just slightly greater than relativistic momentum

• An object travelling at 1.00c would have an infinite amount of momentum.

The rest mass of an electron is 9.109 × 10^-31 kg. What is the momentum of an electron travelling at a speed 0.985c?

• 5.20 x 10^-30 kgms^-1

• 1.56 x 10^-31 kgms^-1

• 8.97 × 10^-31 kg m s^-1

• 2.69 × 10^-22 kg m s^-1

Twins Jo and Betty build a spaceship capable of travelling at 0.8c. Betty uses the space ship to travel to a star A 6 light years away, while Jo stays back on Earth. How much time does it take Betty to reach star A according to Jo?

• 7.5 years

• 10 years

• 4 years

• 6 years

On the spaceship travelling at 0.8c, what is the distance Betty measures to star A (6 ly away in Earth's reference frame), and much time passes for her to reach the star system?

• The distance is 3.6 lightyears, so it takes her 4.5 years.

• The distance is 6 lightyears which takes her 4.5 years.

• The distance is 5 lightyears, so it takes her 6.25 years.

• The distance is 6 light years which takes her 7.5 years

On arriving at Star A Betty quickly collects some data, then turns the star ship around and heads home the 6 light years at 0.8c. How have the twins aged by the time she gets home?

• Betty has aged 9 years and Jo 15 years

• Jo has aged 9 years and Betty 15 years

• Both twins are have aged by 9 years

• Both twins have aged by 15 years

Since all references frames are equal, what is the apparent paradox about the twin's ages.

• In Jo's reference frame Betty travelling on the spaceship at 0.8c should age faster than Jo.

• In Betty's reference frame, she is standing still and Earth is moving away at 0.8c, therefore Betty will be older than Jo when she returns.

• In Jo's reference frame Betty is moving at 0.8c, therefore the distance she needs to travel is longer than 6 light years.

• Since Betty is travelling at 0.8c her relativistic momentum is less than her Newtonian momentum.

What is the resolution to the paradox, that Jo (on Earth) should age more than Betty (moving away at 0.8c in the rocket) in Jo's reference frame and Betty should age more than Jo in Betty's reference frame (in which Earth is moving away from her at 0.8c)?

• Jo ages more when Betty is travelling away from Earth and Betty ages more on the return trip

• Special relativity only applies to inertial (non-accelerating) reference frames and the rocket accelerates at the beginning and end of its journey.

• Earth cannot move at 0.8c therefore only Jo ages

• Jo's Newtonian momentum is zero so her relativistic momentum is also zero