36. Special Relativity

Lorentz Transformations

Lorentz Transformations | Special Relativity Ch. 3

<p>In a particle accelerator, a neutron is traveling at a speed of 0.7 c, as measured by you in a laboratory. This neutron decays (becoming a proton), ejecting an electron. If you measure the electron’s speed to be 0.5 c, traveling in the same direction as the neutron, what was the relative speed between the electron and neutron when the neutron decayed? Was the electron ejected forward or backwards relative to the neutron’s motion, as “seen” by the neutron?</p>

According to Earth-based observers, the space time coordinates of a collision between two asteroids are <math display='inline'><mrow><mo stretchy='false'>(</mo><mi mathvariant="normal">x</mi><mo>,</mo><mi mathvariant="normal">t</mi><mo stretchy='false'>)</mo><mo>=</mo><mo stretchy='false'>(</mo><mn>3.0</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>11</mn></mrow></msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mo>,</mo><mo rspace="thickmathspace">&#x2062;</mo><mn>450</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">s</mi><mo stretchy='false'>)</mo></mrow></math>. What are the coordinates according to an astronaut moving in the positive x direction at 0.78c<math display="inline"><mrow><mn>0.78</mn><mi mathvariant="normal" class="MathML-Unit">c</mi></mrow></math>?

Introduction to the Lorentz transformation | Special relativity | Physics | Khan Academy

Lorentz Transformations of Position

Evaluating a Lorentz transformation | Special relativity | Physics | Khan Academy

Lorentz Transformations of Velocity

What is the momentum of a proton moving at <math display="inline"><mrow><mn>0.987</mn><mi mathvariant="normal" class="MathML-Unit">c</mi></mrow></math>?

<p>In a lab frame, S, an object crosses a distance of 15 m in 10 s. In an initially aligned frame S', moving at 1000 km/s in the x-direction relative to S, how far a distance does the object have to travel, and in what time does it travel the distance?</p>

For a particle moving <math display=“inline”><mrow><mn>0.954</mn><mi>c</mi></mrow></math>. what percent of its total energy is kinetic energy?

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