Lesson: Relativistic Kinetic Energy High School Physics

Physics

In this lesson, we will learn how to calculate the relativistic kinetic energy of massive objects moving relative to an observer.

Worksheet: 10 Questions

Q1:

The graph shows the kinetic energy, EK, against the speed, 𝑣, of two objects, 𝐴 and 𝐡. The relativistic kinetic energy of object 𝐴 is shown by the red line, whereas the classical kinetic energy of object 𝐡 is shown by the blue line. Object 𝐴 has a rest mass π‘šοŒ  and object 𝐡 has a rest mass π‘šοŒ‘. The speed of light, 𝑐, is defined to be 1.

Which object has a greater rest mass?

At a speed of 0.8𝑐, the classical kinetic energy of object 𝐡 has the same value as the relativistic kinetic energy of object 𝐴. The formula π‘š=2π‘šο€Ώο„ž1𝑣+1π‘£βˆ’π‘£βˆ’1π‘£ο‹οŒ‘οŒ οŠͺοŠͺ can be used to work out the rest mass of object 𝐡 from the rest mass of object 𝐴, where 𝑣=0.8𝑐. If π‘š=1 kg, what is the rest mass of object 𝐡?

Q2:

A spaceship moves at a speed of 0.1𝑐 relative to Earth. The rest mass of the spaceship is 200,000 kg. What is the relativistic kinetic energy of the spaceship in the rest frame of Earth? The spaceship is far enough away from Earth such that the effect of Earth’s gravity can be ignored. Give your answer to 3 significant figures.

Q3:

Two spaceships are moving through deep space. The relativistic kinetic energy of spaceship A relative to spaceship B is 4.51Γ—10 J. The speed of spaceship A relative to spaceship B is 0.05𝑐. What is the mass of spaceship A? Give your answer to 3 significant figures.

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