# 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 -axis shows the speed as and the -axis shows the momentum, , divided by the speed of light, . Use the formula to find the rest mass of the object.

**Q2: **

An object is traveling at 75% of the speed of light in a frame . 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 kgā m/s
- B kgā m/s
- C kgā m/s
- D kgā m/s
- E 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
- B
- C
- D
- E

**Q4: **

The graph shows how relativistic momentum varies with speed for two objects with different rest masses. The -axis shows the speed of the objects as and the -axis shows the momentum of the objects, , divided by the speed of light, . 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 relative to the particle accelerator. Its relativistic momentum in the rest frame of the accelerator is kgā m/s. What is the rest mass of the particle?

- A kg
- B kg
- C kg
- D kg
- E kg

**Q6: **

A pion in a particle accelerator has a speed of 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 -axis shows the speed as and the -axis shows the momentum divided by the speed of light, . 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 . At speeds less than , 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 relative to Earth. What is the relativistic momentum of the spaceship relative to Earth?

- A kgā m/s
- B kgā m/s
- C kgā m/s
- D kgā m/s
- E kgā m/s

**Q9: **

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

- A kgā m/s
- B kgā m/s
- C kgā m/s
- D kgā m/s
- E kgā m/s

**Q10: **

In an inertial reference frame , an object has a speed of and a relativistic momentum of kgā m/s. What is its rest mass? Answer to one significant figure.