Worksheet: Relativistic Momentum

In this worksheet, we will practice calculating the relativistic momentum of massive objects moving relative to an observer.

Q1:

The graph shows how the relativistic momentum of an object varies with speed. The š‘„ -axis shows the speed as š›½ = š‘£ š‘ and the š‘¦ -axis shows the momentum, š‘ , divided by the speed of light, š‘ . Use the formula š‘š = š‘ š‘ Ɨ 1 š›¾ š›½ ļŠ¦ to find the rest mass of the object.

Q2:

An object is traveling at 75% of the speed of light in a frame š‘† . The object has a rest mass of 2 kg. How much greater is the relativistic momentum of the object than the classical momentum of the object? Give your answer to 3 significant figures.

  • A 6 . 8 0 Ɨ 1 0 ļŠ® kgā‹…m/s
  • B 2 . 3 0 Ɨ 1 0 ļŠ® kgā‹…m/s
  • C 4 . 5 0 Ɨ 1 0 ļŠ® kgā‹…m/s
  • D 5 . 7 9 Ɨ 1 0 ļŠ® kgā‹…m/s
  • E 9 . 0 0 Ɨ 1 0 ļŠ® kgā‹…m/s

Q3:

At what speed is the relativistic momentum of an object equal to twice its classical momentum? Give your answer to 3 significant figures.

  • A 0 . 7 0 7 š‘
  • B 0 . 7 5 0 š‘
  • C 0 . 8 6 6 š‘
  • D 0 . 5 7 7 š‘
  • E 0 . 5 0 0 š‘

Q4:

The graph shows how relativistic momentum varies with speed for two objects with different rest masses. The š‘„ -axis shows the speed of the objects as š›½ = š‘£ š‘ and the š‘¦ -axis shows the momentum of the objects, š‘ , divided by the speed of light, š‘ . The red line shows the relativistic momentum of object A and the blue line shows the relativistic momentum of object B. What is the ratio of the rest mass of object B to the rest mass of object A?

Q5:

A kaon in a particle accelerator has a speed of 0 . 9 9 š‘ relative to the particle accelerator. Its relativistic momentum in the rest frame of the accelerator is 1 . 8 5 Ɨ 1 0 ļŠ± ļŠ§ ļŠ® kgā‹…m/s. What is the rest mass of the particle?

  • A 1 . 3 5 Ɨ 1 0 ļŠ± ļŠØ ļŠ­ kg
  • B 6 . 2 5 Ɨ 1 0 ļŠ± ļŠØ ļŠ® kg
  • C 8 . 7 9 Ɨ 1 0 ļŠ± ļŠØ ļŠ® kg
  • D 1 . 2 4 Ɨ 1 0 ļŠ± ļŠØ ļŠ® kg
  • E 6 . 2 3 Ɨ 1 0 ļŠ± ļŠØ ļŠ­ kg

Q6:

A pion in a particle accelerator has a speed of 0 . 9 9 8 š‘ relative to the particle accelerator. Its relativistic momentum in the rest frame of the accelerator is 2,210 MeV/c. What is the rest mass of the particle? Give your answer to 3 significant figures.

Q7:

The graph shows how both the classical momentum and the relativistic momentum of an object vary with speed. The š‘„ -axis shows the speed as š›½ = š‘£ š‘ and the š‘¦ -axis shows the momentum divided by the speed of light, š‘ . The object has a mass of 1 kg. The blue line shows the classical momentum of the object and the red line shows the relativistic momentum of the object.

Which of the following statements is true?

  • AThe magnitude of the relativistic momentum is greater than the magnitude of the classical momentum at any speed.
  • BThe magnitude of the relativistic momentum and the magnitude of the classical momentum are equal at any speed.
  • CThe magnitude of the classical momentum is greater than the magnitude of the relativistic momentum at any speed.
  • DThe magnitude of the relativistic momentum is greater than the magnitude of the classical momentum at speeds greater than 0 . 2 š‘ . At speeds less than 0 . 2 š‘ , the relativistic momentum is equal to the classical momentum.

Q8:

A spaceship traveling from Earth to the Gliese 832 system has a rest mass of 80,000 metric tons. It travels at a speed of 0 . 8 š‘ relative to Earth. What is the relativistic momentum of the spaceship relative to Earth?

  • A 5 . 3 Ɨ 1 0 ļŠ§ ļŠ¬ kgā‹…m/s
  • B 9 . 6 Ɨ 1 0 ļŠ§ ļŠ¬ kgā‹…m/s
  • C 4 . 3 Ɨ 1 0 ļŠ§ ļŠ¬ kgā‹…m/s
  • D 3 . 2 Ɨ 1 0 ļŠ§ ļŠ¬ kgā‹…m/s
  • E 1 . 2 Ɨ 1 0 ļŠ§ ļŠ­ kgā‹…m/s

Q9:

In an inertial reference frame š‘† , an object with a rest mass of 5 kg has a velocity of 0 . 1 š‘ . What is the relativistic momentum of the object in frame š‘† ? Give your answer to 5 significant figures.

  • A 1 . 5 1 5 2 Ɨ 1 0 ļŠ® kgā‹…m/s
  • B 1 . 5 8 1 2 Ɨ 1 0 ļŠ® kgā‹…m/s
  • C 1 . 5 0 7 6 Ɨ 1 0 ļŠÆ kgā‹…m/s
  • D 1 . 6 6 6 7 Ɨ 1 0 ļŠ® kgā‹…m/s
  • E 1 . 5 0 7 6 Ɨ 1 0 ļŠ® kgā‹…m/s

Q10:

In an inertial reference frame š‘† , an object has a speed of 0 . 6 š‘ and a relativistic momentum of 1 . 8 Ɨ 1 0 ļŠ® kgā‹…m/s. What is its rest mass? Answer to one significant figure.

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