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‘Ć—1š›¾š›½ļŠ¦ 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.

  • A2.30Ɨ10ļŠ® kgā‹…m/s
  • B6.80Ɨ10ļŠ® kgā‹…m/s
  • C5.79Ɨ10ļŠ® kgā‹…m/s
  • D4.50Ɨ10ļŠ® kgā‹…m/s
  • E9.00Ɨ10ļŠ® 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.

  • A0.577š‘
  • B0.866š‘
  • C0.750š‘
  • D0.500š‘
  • E0.707š‘

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 0.99š‘ relative to the particle accelerator. Its relativistic momentum in the rest frame of the accelerator is 1.85Ɨ10ļŠ±ļŠ§ļŠ® kgā‹…m/s. What is the rest mass of the particle?

  • A6.25Ɨ10ļŠ±ļŠØļŠ® kg
  • B6.23Ɨ10ļŠ±ļŠØļŠ­ kg
  • C8.79Ɨ10ļŠ±ļŠØļŠ® kg
  • D1.24Ɨ10ļŠ±ļŠØļŠ® kg
  • E1.35Ɨ10ļŠ±ļŠØļŠ­ kg

Q6:

A pion in a particle accelerator has a speed of 0.998š‘ 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 and the magnitude of the classical momentum are equal at any speed.
  • BThe magnitude of the relativistic momentum is greater than the magnitude of the classical momentum 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 0.2š‘. At speeds less than 0.2š‘, 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 0.8š‘ relative to Earth. What is the relativistic momentum of the spaceship relative to Earth?

  • A3.2Ɨ10ļŠ§ļŠ¬ kgā‹…m/s
  • B5.3Ɨ10ļŠ§ļŠ¬ kgā‹…m/s
  • C9.6Ɨ10ļŠ§ļŠ¬ kgā‹…m/s
  • D4.3Ɨ10ļŠ§ļŠ¬ kgā‹…m/s
  • E1.2Ɨ10ļŠ§ļŠ­ kgā‹…m/s

Q9:

In an inertial reference frame š‘†, an object with a rest mass of 5 kg has a velocity of 0.1š‘. What is the relativistic momentum of the object in frame š‘†? Give your answer to 5 significant figures.

  • A1.5812Ɨ10ļŠ® kgā‹…m/s
  • B1.6667Ɨ10ļŠ® kgā‹…m/s
  • C1.5152Ɨ10ļŠ® kgā‹…m/s
  • D1.5076Ɨ10ļŠÆ kgā‹…m/s
  • E1.5076Ɨ10ļŠ® kgā‹…m/s

Q10:

In an inertial reference frame š‘†, an object has a speed of 0.6š‘ and a relativistic momentum of 1.8Ɨ10ļŠ® kgā‹…m/s. What is its rest mass? Answer to one significant figure.

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