Question

Work out the following a) Find β = v/c for a person walking at 3 mile/hr and a truck moving at 65 mile/hr. (b) Find γ-1, where γ¡s the relativistic factor γ 1/ VI-B" for the velocities in (a). You should expand γusing the small velocity approximation to get the best results

Answer 1

Step-by-step explanation:

It is given that,

Speed of the person, v = 3 mile/hr = 1.34 m/s

Speed of the truck, v' = 65 mile/hr = 29.05 m/s

(a) Since,
`\beta =(v)/(c)`

For the person,
`\beta =(1.34)/(3* 10^8)=4.47* 10^(-9)`

For the truck,
`\beta =(29.05)/(3* 10^8)=9.68* 10^(-8)`

(b) The relativistic factor is given by :

`\gamma=(1)/(√(1-\beta^2))`

For very small velocity,
`\beta<<1`

`\gamma=(1-\beta ^2)^(-1/2)\approx 1+(1)/(2)\beta ^2`

`\gamma-1=(\beta^2)/(2)`

For the person :

`\gamma-1=((4.47* 10^(-9))^2)/(2)=9.99* 10^(-18)`

For the person :

`\gamma-1=((9.68* 10^(-8))^2)/(2)=4.68* 10^(-15)`

Hence, this is the required solution.