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$\bullet$ (a) At what speed does the momentum of a particle differby 1.0$\%$ from the value obtained with the nonrelativisticexpression $m v ?$ (b) Is the correct relativistic value greater orless than that obtained from the nonrelativistic expression?

greater

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

University of Washington

Simon Fraser University

Hope College

University of Winnipeg

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.

01:00

The relativistic momentum …

00:50

At what speed is the momen…

09:53

At what speed will the rel…

01:59

What speed must a particle…

04:35

The non relativistic expre…

08:45

$\bullet$ Using both the n…

01:04

What is the relativistic m…

06:32

Find the speed of a partic…

01:58

The nonrelativistic expres…

Okay, So in this problem, we have to calculate the first item. They speed off well active relativistic particle. And we know that the difference in the Momenta MME in the relativistic momentum with the non relativistic mo mental off this particle should be just one percent off the momentum. So 1% off him v. Okay, So first of all, before we calculate anything, let's think about what is relativistic Momentum of a particle is just goma in the and we know that this is equal to envy. Divided by one miners the square C square in the square root. And we know that thes denominator. And here iss lesser in one which implies that there were lots of mystic mo mentum should be greater then I envy. That's we're right. This should be greater than envy. So knowing that the relativistic mo mentum should be greater and the no relativistic mo mentum, we can say looking to this condition, the problem gives us in here and that let's put in here that they're no The relativistic mo mentum is just 1% of envy plus envy. So this is give us This is gives us 1.1 empty. And that's the relativistic mo mental we should use in this particular problem. And remember that the relativistic momento is defined as gamma envy. We can say them that gamma is equal 1.1 Just have to look dis factor. And here So we know gam er is just one minus the square c square. All this in this crab bridge 1.1 If we rearrange this equation being gonna have for they speed Niekro's see square root of one minus one, divided by 1.1 square in the square root. So after calculating this, we have for d speed off this particle and the first answer of this problem us. Let's see 0.14 See, that's gives us precisely 4.2. I'm Stan to the power off seven meters per second. That's the answer to the first item. The second item. We just need to remember what I say early that the relativistic mo mentum should be greater then envy. So that's the answer to the second item. The second item. We just need to say that the relativistic mo mentum greater then in no relativistic mo mentum. And that's the final answer. Thanks for what

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