A pole of proper length 90 m is travelling directly toward a barn of proper leng

Question

A pole of proper length 90 m is travelling directly toward a barn of proper length 30 m. At what speed
must the pole be travelling with respect to the barn in order for it to just fit inside, according to an
observer standing in the barn? What is the length of the barn according to an observer travelling with the
pole?
3 A particle of rest mass m0 has a relativistic mass equal to 3m0 (i.e. 3 times the rest mass).
(a) What is the value of the Lorentz gamma factor associated with its motion?
(b) What is its kinetic energy, K, in terms of its rest energy E0? (Express the kinetic energy as a multiple
of E=m0c^2).

Explanation / Answer

length of pole (on barn) =actual length of pole*1-vwrt barn2/c2;

30 = 90*1-vwrt barn2/c2

vwrt barn= 0.942 c;

length of barn (on pole) = actual length of barn *1-0.942c2/c2;

length of barn (on pole) = 30*0.3356 =10.0683 m ;

3.answer

reletivistic mass = m0/1-v2/c2;

3 = 1/1-v2/c2 ; --------------->lorentz gamma factor = 3

v= 0.9428 c;

reletivistic KE = 3m0*(0.9428c)2 =2.66m0c2 ;

rest energy =m0c2 ;

so reletivistic KE = 2.66 times of rest energy

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