Past paper question.. (1 Viewer)

[d.i.m.e Babii]

A muon at rest has an average lifetime of 10^-6s. A muon travelling at high speed in a particle accelerator is found to have a lifetime of 2x10^-6s. What is the approximate speed of the muon?

The answer is 0.87c
But I have no clue how they got that answer.
What equation are you suppose to use?
and where does the c come in?

 

[Riviet]

Use the time dilation equation.

 

[insert-username]

The time dilation question is: t_v = t₀/√(1 - v²/c²)

Our rest time is 10^-6s, and our dilated time is 2 x 10^-6s. We now put those values into the formula and solve for v².

2x10^-6 = 10^-6/√(1 - v²/c²)

2 = 1/√(1 - v²/c²) (divide though by 10^-6)

√(1 - v²/c²) = 1/2 (multiply through by √(1 - v²/c²))

1 - v²/c² = 1/4 (square both sides)

v²/c² = 3/4 (rearrange the equation)

v² = 3/4c² (divide through by c²)

v = √3/2 x c (take the square root of both sides)

= 0.87c (to 2 decimal places, where c is the speed of light - a constant, so it can be left there)


I_F

 

[d.i.m.e Babii]

Thank heaps!!!!

Can't believe all that working out for ONE mark from multiple choice..

*sigh*




<3 d.i.m.e Babii

 

[shsshs]

cld some1 do this one:

two satellites have altitudes of 400 and 4000km respectively. Take R to be the avg radius of orbit and T as the period for one orbit. The ratio (R^3/T^3) of the first satellite compared to the second one is...?

all i can gather is r^3/t^2 is constant.

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also, when doing a practical, how do u draw the line of best fit, do you just guess where the best line is? I heard someone say you draw 2 lines of WORST fit? and then something else

 

[Riviet]

also, when doing a practical, how do u draw the line of best fit, do you just guess where the best line is? I heard someone say you draw 2 lines of WORST fit? and then something else

I would draw a line that has an equal number of points on each side of the line, and try to get as many points on the line itself. Keep in mind that you should ignore any obvious outliers when determining your line of best fit.