Problem

Suppose a particle called a kaon is created by co…

02:44

Problem 3 Medium Difficulty

Particles called $\pi$ -mesons are produced by accelerator beams. If these particles travel at $2.70 \times 10^{8} \mathrm{m} / \mathrm{s}$ and live $2.60 \times 10^{-8} \mathrm{s}$ when at rest relative to an observer, how long do they live as viewed in the laboratory?

Answer

$\Delta t=5.97 \times 10^{-8} \mathrm{s}$

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Physics 103

College Physics for AP® Courses

Chapter 28

Special Relativity

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Video Transcript

well relative to an observer, a pressed that we lost you to buy me zones. Well, the is equal to 2.70 Multiply by tend to the power eight meter per second. Now let's multiply and divide. Uh, this number. Oh, let's see. Body for we have the is equal to to find 70 multiplied by 10 to the power gate multiplied by C divided by divided by three point 00 multiplied by 10 to the power eight. And we is equal to zero point 900 times the speed off light. Well, the life off the by me zones when they pressed relative to an observer Yeah, the proper time is Delta t not. Well, don't. The team mark is the proper time is equal to 2.60 multiplied by 10 to the power minus eight seconds. And we know that they're like mystic factor. Gamma is given by one divided by r squared. Rode off one minus. We divided by, uh, see whole square. Uh, this is C uh, hold should be divided by sea. Hold square on DDE here. See? Is off speed of light and, uh, the also no date are Delta T Oh, it is dilated. Time is equal to delta t not a proper time divided by our spare loot off one minus. We divided by sea hold square. And, uh and we noted gamma is equal to one divided by a squared Rudolph one minus. We divided by c all square, be divided by sea whole square and therefore he have Gamma is equal to one divided by square root off one minus a week. Well, we is little point 0.900 times the speed of light divided by sea, whole square and gamma is equal to one divided by square root off one a minus 0.9 00 whole script C square gets cancelled, it see sphere and we're left with one minus 0.90 and in his square as well. And gamma is equal to one divided by a squared Rudolph one minus 0.81 And this gives us two point 294 All right, on dhe now are the life off the by. Miss Jones is a building the laboratory is given by Delta. T is equal to relax. Mystic factor times are Delta t not Delta t knock is the proper time, and therefore we have a delta T is equal to a two point 294 Is the relativistic factor multiplied by? We have Delta t not. And don't the teen Audi's, um well, Delta t not here. We have, uh, let me find it. Well, uh, don't Latino. It's 2.602 point 60 multiplied by 10 to the power minus eight seconds. And therefore delta t I doubt it. He is a cold too. 5.97 5.97 multiplied by 10 to the dollar minus eight seconds.

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