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\bullet A proton (rest mass $1.67 \times 10^{-27} \mathrm{kg}$ ) has total energy thatis 4.00 times its rest energy. What are (a) the kinetic energy ofthe proton; (b) the magnitude of the momentum of the proton;(c) the speed of the proton?

$v=0.968 \mathrm{c}$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

06:06

A proton (rest mass $1.67 …

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A proton (rest mass 1.67 $…

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A proton'$ rest mass …

02:22

(II) Calculate the speed o…

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a. What are the momentum a…

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A proton moving with a con…

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A proton moves with a spee…

01:07

Consider a proton moving a…

02:27

A proton has a rest energy…

So in this problem, we have a problem with arrest. Mess off one point 67 times 10 to the power. Let's see the power of minors. 27 Dan with the power off miners 27 kilograms, it's his arrest mess and we want to calculate first the connect e energy, the relativistic connecting energy off this broughtem. Second, we want to calculate what is the magnitude off the mo mentum broughtem? Unless we want to calculate what is the speech off this product? Um and the only thing that problem gives us is that the photo realistic relativistic energy is four times the arrest Energy reaches M. C Square as we know. So this is the only information that we have in this problem. So let's begin with the connect energy. We know by definition that the connective energy can act. Energy is just the relativistic energy minus M C square, which is the rest mess, the rest energy. So the connecting energy in this problem should be just for in C square minus M C square, which gives us three m c square. We have the mass of the rotten and the speed of light. We already know. So this is just 4.5 times 10 to the power off my understand house. That's the answer. The first ladder is the connect Relativistic Anarchy Energy. So now let's calculate the mo mentum. We want to cover it now The magnitude of the mo mentum. We know that in the reference frame off the Brockton Toto energy is given by E square, which is the relativistic energy equals M C square. Oh, this square of us E c. Square. So the momentum is just, Let's see, we know that the energy is for M C Square. So this is going to be for M C Square. All these square equals, uh, let's see equals n c square square plus B c square. So this is just 16. My no swung in C square in the square it close it close P square C square. So we can say that this is 15 actually square root of 15. The multiplies and C square equals E c. We can cut one or the one off the speed of light and then we have that. The Momenta MB is just squarer to 15 EMC. So calculating this we get one point 94 times 10 to the power off minus 18 kilograms meters for a second. That's the answer to the second letter. Now let's calculate finally, the speed off the that's calculate the speed of the proctor. Well, we know that in the reference frame off the laboratory, a person that is not a problem. We can say that the total energy the relativistic daughter energy to define as gamma M C Square. And we know that gamma is just squared, divided by one minus the square C square. Oh, this in the square root. So if we calculate ISS, we know that the relativistic energy is just four m c. Square, so this is equal to gamma M C square, so we can say that gamma should be equal to four. So if we elevated both sides an invert, the fractions we have one minus the square C square equals one divided by 16. So the arranging desecration we can see that V e close 15 divided by 16 in the square root, then multiply. See? So this is just zero point 96 eight. See, it's pretty close to dispute a flight, as we can see. So that's the final answer to this problem. That's all. Thanks for watching

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