Question

A particle travels at 0.14c. By what percentage will a calculation of its momentum be wrong if you use the classical formula?

Express your answer using two significant figures.

p−prelprel = ? %

B- Repeat for

0.58c.

Express your answer using two significant figures

p−prelprel = ? %

Answer 1

(A) velocity of a particle, v = 0.14 c

we know that, classical momentum is given as -

p₀ = m v                                                                { eq.1 }

Relativistic momentum is given as -

p_rel = m v                                                                                                 { eq.2 }

The percent difference will be given as,

( m v - m v) / m v = ( - 1) /

1 - (1 / )                                                                                                           { eq.3 }

where, = 1 / 1 - (v / c)²

inserting the value of 'v'

= 1 / 1 - (0.14)²

= 1 / 1 - (0.0196)

= 1 / (0.99015)

= 1.0099

now, we have 1 - (1 / 1.0099) = 0.009802 or 0.98 %

(B) For v = 0.58c

using eq.3,    1 - (1 / )    

where, = 1 / 1 - (v / c)²

inserting the value of 'v'

= 1 / 1 - (0.58)²

= 1 / 1 - (0.3364)

= 1 / (0.81461)

= 1.2275

now, we have 1 - (1 / 1.2275) = 0.185 or 18.5 %