An unstable particle with a mass equal to 3.34 10-27 kg is initially at rest. Th

Question

An unstable particle with a mass equal to 3.34 10-27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.987c and -0.869c, respectively. Find the masses of the fragments. (Hint: Conserve both mass-energy and momentum.)
m(0.987c) =____ kg
m(-0.869c) =____ kg

Explanation / Answer

Energy conservation: m1c^2/sqrt(1-.98^2) + m2c^2/sqrt(1-.870^2) = Mc^2 = 3.34*10^-27*c^2 (I) Momentum conservation: m1*.98c/sqrt(1-.98^2)-m2*.87c/sqrt(1-.… (II) (II) m2 = sqrt(1-.87^2)/sqrt(1-.98^2).98/.87m1 (a) (I)+(a) => m1/sqrt(1-.98^2) + m1 /sqrt(1-.98^2).98/.87 = M m1 = M * sqrt(1-.98^2)./(1+98/.87 ) = 3.125 10^-28 kg likewise: m2 = M*sqrt(1-.87^2)/(1+.87/.98) = 8.723 10^-28 kg Please note how the ridiculous notion of 'relativistic' or 'dilated' mass induces the first answerer into a completely wrong interpretation of the question. Mass is a fixed quantity and m/v(1-(v/c)^2 ) is energy (up to the constant c^2)

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