1) A spaceship of triangular shape, having a length twice itswidth, is capable o

Question

1) A spaceship of triangular shape, having a length twice itswidth, is capable of relativistic speeds. How fast would ithave to move so that to a stationary observer its length wouldequal its width?

      a. 0.500 c  b. 0.750 c   c. 0.866 c   d.This is not possible.

2) At whatspeed must an object be moving in order that it has a kineticenergy 1.50 times its rest energy? (c = 3.00 ´108 m/s)

      a. 1.91 ´ 108m/s   b. 2.52 ´ 108 m/s   c.2.75 ´ 108 m/s   d. 2.90 ´108 m/s

3) An electronand a positron both of rest energy 0.511 MeV slowly drift togetherand annihilate into two gamma ray photons. What is the wavelengthof each of the photons? (h = 6.63 ´10-34 J×s, c = 3.00 ´108 m/s, and 1 eV = 1.60 ´10-19 J)

      a. 1.21 ´10-12 m   b. 2.43 ´10-12 m   c. 4.86 ´10-12 m   d. 9.72 ´10-12 m

4) A proton (mass = 1.67 ´10-27 kg) has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 1.00%, what isthe minimum uncertainty in its position? (h = 6.63 ´10-34 J×s, 1 eV = 1.6 ´10-19 J)

a. 9.08´ 10-13 m   b. 2.28 ´10-13 m   c. 9.08 ´10-14 m   d. 5.64 ´10-14 m

Explanation / Answer

We know the formula the proper length is                       L = Lo[1 - (v2 / c2)]                       L= 2L[1 - (v2 / c2)]                      1 / 2 = [1 - (v2 / c2)]                     [1- (v2 / c2)] = 1 / 4                          v2 / c2 = 3/4                             v = (3/4) c                               = 0.866c

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