An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles.

Question

An unstable nucleus of mass 1.7 ✕ 10⁻²⁶ kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m₁ = 1.8 ✕ 10⁻²⁷ kg, moves in the positive y-direction with speed v₁ = 5.0 ✕ 10⁶ m/s. Another particle, of mass m₂ = 7.0 ✕ 10⁻²⁷ kg, moves in the positive x-direction with speed v₂ = 3.6 ✕ 10⁶ m/s. Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) 

a) magnitude: ____ m/s

b) direction: ____  ° counterclockwise from the +x-axis

Answer 1

So Kat J.,

Momentum is conserved, in each axis of your frame of reference. Calculate the given momenta of the two particles; the third particle must have a net momentum to exactly oppose their sum. Calculate that as a vector in the x-y plane.

-- Cheers, --Mr. d.

P.S. Momentum is always conserved, in each orthogonal axis, in a non-rotating frame of reference. That includes angular momentum, too. But the same is NOT necessarily true for kinetic energy, because of the v^2 calculation involved.