- #1

chef99

- 75

- 4

## Homework Statement

**A muon has a lifetime of 2.20 x10**

^{-6}s when at rest, after which time it decays into other particles.**a) Ignore any effects of relativity discussed in this section. If the muon was moving at 0.99c, how far would it travel before decaying into other particles, according to Newtonian mechanics?**

b)

**How long would the muon last, according to an observer in the earth’s frame of reference who viewed the muon moving at 0.99c?**

c)

2. Homework Equations

c)

**How far would the muon actually travel, when viewed moving at 0.99c?**

d)d)

**Compare the two distances traveled. Explain why this type of evidence is excellent support for the theory of relativity.**

2. Homework Equations

d = vt

Δtm = Δts / 1-√v

^{2}/c

^{2}

## The Attempt at a Solution

a)

d = (0.99c)(3.00 x10

^{8}m/s)

d = 2.97 x10

^{-8}m/s

(2.97 x10

^{-8}m/s)(2.2 x10

^{-6}s)

= 653.4 m

b) Δtm = Δts / 1-√v

^{2}/c

^{2}

Δtm = 2.2 x10

^{6}/ √1- 0.9801

Δtm = 1.56 x10

^{-5}s

The muon will last 1.56 x10

^{-5}s in the earth’s frame of reference, moving at 0.99c

c) Using special relativity, the muon would last for d

_{SR}= vτ, where τ is now the relativistic lifetime of the muon.

d

_{SR}= vτ

d

_{SR}= (0.99c)(3.00 x10

^{8}m/s)(1.56 x10

^{-5}s)

d

_{SR}= 4633.2 m

d)

These results are a good demonstration of relativity because they show that time dilation becomes significant as the velocity approaches the speed of light.

I'm just not sure if I did b) and c) right, in c) when it says "How long will it last", I assume that means how many seconds, but I could be wrong. It seemed logical in c) to use the same equation as a) but simply change the value of τ to the relativistic value, but as I haven't had to use this equation before I'm not sure if it is the right one to be using. I would appreciate any feedback