In the alternate universe, how fast must an object be moving...

Name: Problem 74, Chapter 37: University Physics with Modern Physics
Uploaded: 2019-05-03T03:02:57-08:00
Duration: 3 min
Channel: Ceren Uzun
Description: In the alternate universe, how fast must an object be moving for it to have a kinetic energy equal to its rest mass? (a) 225 m/s; (b) 260 m/s; (c) 300 m/s; (d) The kinetic energy could not be equal to the rest mass.

In the alternate universe, how fast must an object be moving for it to have a kinetic energy equal to its rest mass? (a) 225 m/s; (b) 260 m/s; (c) 300 m/s; (d) The kinetic energy could not be equal to the rest mass.

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Key Concepts

Rest Mass Energy

Rest mass energy is the intrinsic energy represented by an object's mass, defined by the equation E = mc². This concept serves as a fundamental reference point for energy comparisons in physics, particularly in relativity, where it sets the scale against which other forms of energy (like kinetic energy) are measured.

Kinetic Energy in Special Relativity

In the framework of special relativity, kinetic energy is expressed as the difference between the total relativistic energy (?mc²) and the rest mass energy (mc²). Unlike its classical counterpart, this form of kinetic energy accounts for relativistic effects that become significant as an object's speed approaches the speed of light.

Lorentz Factor

The Lorentz factor, given by the formula ? = 1/?(1 - v²/c²), quantifies the degree of time dilation, length contraction, and relativistic mass increase experienced by an object moving at a velocity v relative to the speed of light c. It plays a crucial role in calculating the total energy of an object and, by extension, its relativistic kinetic energy.

Transcript

00:01 This is chapter 37 problem number 74.

00:03 We're given an alternate universe where the speed of light is one millionth of what we have on earth.

00:12 So let's calculate that because that's an important part of the problem.

00:17 So we are to actually take this speed of light to be three times 10 to power of 2 meters per second, which would be 300 meters per second.

00:30 Imagine this is the speed of light in an alternate universe.

00:33 And the question is what happens if the rest energy e not equals to the kinetic energy of this particle, then what would be the speed of that particle? so for this to happen, as you know, theoretically, well, the rest energy would be m not, the rest mass c squared equals to m not c squared for the kinetic energy term.

00:58 We have gamma minus 1, the gamma factor minus 1.

01:04 So this is the condition which we were given.

01:08 So i am not c squared and not 6 squared.

01:10 They're going to cancel each other out.

01:11 So what we have here, gamma factor minus 1 is going to be equal to 1.

01:17 Then gamma is going to be equal to 2.

01:19 As you know, gamma is 1 over square root of 1 minus v squared over c squared.

01:24 And we're trying to get to v.

01:25 That's why i'm going to take the inverse of this...