Multiconcept Exercise 28.44 Part A Suppose a starship had a mass of 1.55x109 kg

Question

Multiconcept Exercise 28.44 Part A Suppose a starship had a mass of 1.55x109 kg and was initially at rest. If its "matter-antimatter engines" produced photons from electron-positron annihilation and focused them to travel backward out from the ship, how many photons would they have to emit to reach 0.300 % of the speed of light? [Hint: Use conservation of linear momentum and remember that relativity is not needed here. (Why?)] 38 photons Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining

Explanation / Answer

energy of photon = 2(0.511 MeV)

and p = h / E = (6.626 x 10^-34) / (2 x 0.511 x 10^6 x1.6 x 10^-19)

= 4.052 x 10^-21 kg m/s

Applying momentum conservation,

pi = pf

0 = n (4.052 x 10^-21) - ((1.55 x 10^9 - n(2 x 9.109 x 10^-31))(0.003 x 3 x 10^8))

{ relativity will not be used because v = 0.003c , v is less compared to c}

n (4.052 x 10^-21 + 1.64 x 10^-24) = 1.555 x 10^9 x 0.003 x 3 x 10^8  

n = 3.44 x 10^35 photons

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