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photoshop1234 [79]
3 years ago
10

Pions have a half-life of 1.8 x 10^-8 s. A pion beam leaves an accelerator at a speed of 0.8c. What is the expected distance ove

r which half the pions should decay?
Physics
1 answer:
Nuetrik [128]3 years ago
5 0

Answer:

the expected distance is 4.32 m

Explanation:

given data

half life time = 1.8 × 10^{-8} s

speed = 0.8 c = 0.8 × 3 × 10^{8}

to find out

expected distance over

solution

we know c is speed of light in air is 3 × 10^{8} m/s

we calculate expected distance by given formula that is

expected distance = half life time × speed   .........1

put here all these value

expected distance = half life time × speed

expected distance = 1.8 × 10^{-8} ×  0.8 × 3 × 10^{8}

expected distance = 4.32

so the expected distance is 4.32 m

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a.  v=3.11mls, 29.4^{0}

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Momentum of player 1 p_{1} =mv=95kg*5m/s\\p_{1} =475kgm/s\\

Momentum of player 2 p_{2} =mv=90kg*3m/s\\p_{1} =270kgm/s\\

Hence the total momentum p_{12}=p_{1}+p_{2}\\

Note, since the direction of movement before collision is due south and  due north respectively we have to represent the velocity using the rectangular coordinate

Hence  p_{12}=(m_{1}+m_{2})v=p_{1}i+p_{2}j\\

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v=2.57i+1.45j\\

solving for the resultant velocity, we have

v=\sqrt{2.75^{2} +1.45^{2}}\\ v=3.11mls

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\alpha =tan^{-1}=\frac{v_{j} }{v_{i}}\\  \alpha =tan^{-1}=\frac{1.45}{2.57}\\\alpha =29.4^{0}

b. to calculate the decrease in total kinetic energy, before collision, the total kinetic was

K.E_{initial} =\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}.\\K.E_{initial} =((1/2)*95*5^{2})+((1/2)*90*3^{2})\\K.E_{initial} =1187.5+405\\K.E_{initial} =1592.5J\\

And the final kinetic energy after collision is

K.E_{final} =\frac{1}{2}(m_{1}+m_{2} )v^{2}\\  K.E_{final} =\frac{1}{2}(95+90)* 3.11^{2}\\ K.E_{final} =894.7J

The decrease in Kinetic energy is

K.E =K.E_{final}- K.E_{initial}=894.7-1592.5

K.E =-697.8J

The negative sign indicate a decrease in Kinetic energy

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