Before Collision After nit in nin 2.95v Vn,final = ? Two particles, of mass m an

Question

Before Collision After nit in nin 2.95v Vn,final = ? Two particles, of mass m and mass nm, undergo a head-on, fully elastic collision. (Here n is just a unitless number.) Before colliding the particles approach one another with equal speed v. Snapshots of the particles elfore,during, and aier the oilisionaritupe the particle After the collision the first particle moves away with speed 2.95v in the exact opposite direction, and the velocity of the second particle is unknown. What is the value of n? Number

Explanation / Answer

given two particles of mass m, nm
head on fully elastic collision
inital velocity = v, -v

after collsiion velocity of particle 1 = -2.95v
velocity of othe rparticle = u

hence from the definition of coefficient of restitution for fully elastic collsions
(v + v)/(u + 2.95v) = 1
2v = u + 2.95v
u = -0.95v

also, from conservation of moemtnum
mv - nm*v = m*(-2.95v) + nm*(-0.95v)
1 - n = -2.95 - 0.95n
n = 79

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