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Chapter 37: Q5P (page 1145)

An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before it decays. Its speed relative to the detector was 0.992c. What is its proper lifetime? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector?

Short Answer

Expert verified

The proper life time for particle is 0.446ps.

Step by step solution

01

Identification of given data

The speed of particle relative to detector is v=0.992c

The length of track is L=1.05mm

The time dilation is used to find the duration for particle before decay from detector.

02

Determination of proper life time before decay of particle

The proper life time for particle is given as:

t0=LV1-vc2

Here, is the speed of light and its value is 3脳108m/s.

Substitute all the values in equation.

t0=1.05mm1m103mm0.992c3脳108m/sc1-0.992cc2t0=0.0446脳10-11st0=0.0446脳10-11s1ps10-12st0=0.446ps

Therefore, the proper life time for particle is 0.446ps .

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Relativistic reversal of events. Figures 37-25a and b show the (usual) situation in which a primed reference frame passes an unprimed reference frame, in the common positive direction of the xand xaxes, at a constant relative velocity of magnitude . We are at rest in the unprimed frame; Bullwinkle, an astute student of relativity in spite of his cartoon upbringing, is at rest in the primed frame. The figures also indicate events Aand Bthat occur at the following spacetime coordinates as measured in our unprimed frame and in Bullwinkle鈥檚 primed frame:

Event Unprimed Primed

AB (xA,tA)(xB,tB) (x'A,t'A)(x'B,t'B)

In our frame, event Aoccurs before event B, with temporal separation鈭�t=tA-tB=1.00渭sand spatial separation鈭�x=xB-xA=400m. Let be the temporal separation of the events according to Bullwinkle. (a) Find an expression for鈭�t'in terms of the speed parameter 尾=vcand the given data. Graph鈭�t'versus 尾for the following two ranges of尾:

(b) 0to0.01( vis low, from 0 to0.01c)

(c) 0.1 to 1 ( vis high, from to the limitc)

(d) At what value of 尾is 鈭�t'=0? For what range of 尾is the sequence of events Aand Baccording to Bullwinkle (e) the same as ours and (f) the reverse of ours? (g) Can event Acause event B, or vice versa? Explain
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