1. A particle of mass m decays into two identical particles that move in opposit

Question

1. A particle of mass m decays into two identical particles that move in opposite directions, each with a speed of 12/13. What is the mass of each of the product particles (expressed as a fraction of m)?

2. Consider a freely floating mirror placed initially at rest in a laser beam. Imagine the mirror to be oriented directly facing the beam so that the mirror reflects the beam back the way it came. Eacy flash of light that rebounds from the mirror has undergone a change in its momentum as a result of the change in direction of its velocity. This means that the mirror must recoil a bit from each rebound to conserve four-momentum. Use conservation of the spacial components of four-momentum to estimate how much power the laser beam would have to have to accelerate a perfect 1-g mirror at a rate of 1 cm/(s^2). (You can assume that the mirror's momentum is essesntially newtonian.) Express your final answer in watts (1 W=1 J/s).

Explanation / Answer

1) let mass is m1 and m2 ::

   then   m1 +m2 =m   ..................(1)

   form conser vation of mementum :: m1*12/13 = m2*12/13

                                                             hence    m1 = m2   ..............(2)

     form (1) and (2) m1 =m2 =m/2

massese are 0.5m ,0.5m

2)    C = speed of light =3*10^8 m/s

let U = power of laser beam .

          p1 =momentum of incident laser beam per unit time = U/C

         p2 = momentum of reflected laser beam per unit time = -U/C

        del(p) = change in momentum per unit time    = -2U/C

    F = force on mirrior = -change in momentum per unit time    = 2U/C

F = 2U/C

m*a =2U/C

0.001*0.01 = 2U/C

       U   = 10^-5*C/2

            = 10^-5*3*10^8/2

            =1500 j/s

power = 1500 J/s = 1500 w

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