Special Relativity: Time Dialation

Classical Mechanics Level 1

Speeds typical of our everyday lives results in the laws of Classical Mechanics; however, when a particle approaches a reasonably high fraction of light speed ( c c ), the time ( t obs t_\text{obs} ) we observe is dilated such that: t o b s = t 1 − v 2 c 2 t_{obs} = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} In an obscure Prussian lab, a positron's velocity ( v v ) was accelerated to 0.6 c 0.6c . If t t , as experienced by the positron, is 200 200 femtoseconds \text{femtoseconds} , what would we observe as the dilated time?

Hint: Find t obs t_\text{obs} in fs \text{fs} .

David's Special Relativity Set


The answer is 250.

David Hontz by David Hontz , 26, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

David Hontz
Dec 20, 2016

t o b s = t 1 − v 2 c 2 = 200 1 − ( 0.6 c ) 2 c 2 = 200 1 − 0.36 c 2 c 2 = 200 1 − 0.36 = 200 0.64 = 250 fs t_{obs} = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{200}{\sqrt{1 - \frac{(0.6c)^2}{c^2}}} = \frac{200}{\sqrt{1 - \frac{0.36c^2}{c^2}}} = \frac{200}{\sqrt{1 - 0.36}} = \frac{200}{\sqrt{0.64}} = \boxed{250 \text{ fs}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I think the problem needs to specify that the answer should be in fm. I tried putting in 250e-15 initially.

Steven Chase - 4 years, 5 months ago

Log in to reply

The problem is designed to only accept integer answers, thus 250e-15 would not count against you. I will stipulate in the problem to maintain the units. Thank you for bringing this up.

David Hontz - 4 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...