Muons & Relativity Homework

• EgpYo
In summary, the conversation discusses the lifetime of a muon and its decay into other particles. It also explores the effects of relativity and how it affects the distance traveled and time elapsed for a muon moving at 0.99c. Through calculations, it is determined that a muon moving at this speed would travel 653.4 meters before decaying, and would last for 0.000015602 seconds according to an observer on Earth. When viewed at 0.99c, the muon would actually travel 463.32 meters. This evidence supports the theory of relativity, as it shows how the perception of time and distance can differ based on the observer's frame of reference.

Homework Statement

A muon has a lifetime of 2.0x10^-6 seconds 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 Earth's frame of reference?
c)How far would the muon actually travel, when viewed moving at 0.99c?
d) Compare the two distances travelled. Explain why this type of evidence is excellent support for the theory of relativity.

Homework Equations

tm = ts/ sqrt(1-v^2/c^2)

The Attempt at a Solution

a) (0.99)(3x10^8) = v
v = 2.97x10^8

v=dt
d = (2.97x10^8)(2.2x19^-6)
d = 653.4 m

b) tm = ts/ (1-v^2/c^2)
tm = 2.2x10^-6/0.141
tm = 0.000015602 s

c) d = vt
= (2.97x19^-6)(1.56x10^-6)
= 463.32 m

d) ?

What are you calculating in (b) ? The expression is not your relevant formula and the calculation is way off !
Fix that and then c and d will be a lot more doable.

EgpYo said:
b) tm = ts/ (1-v^2/c^2)
tm = 2.2x10^-6/0.141
tm = 0.000015602 s

Ok, couple typos there. You forgot the square-root sign. And it might be helpful if you converted your tm into scientific notation.

EgpYo said:
c) d = vt
= (2.97x19^-6)(1.56x10^-6)
= 463.32 m

The (2.97x19^-6) looks like you intended to write (2.97x10^8) but your fingers got away from you.
Check the (1.56x10^-6) .