Two particles approach each other with equal and opposite speed v. The mass of o

Question

Two particles approach each other with equal and opposite speed v. The mass of one particle is m, and the mass of the other particle is nm, where n is just a unitless number. After the collision the first particle moves in the exact opposite direction with speed 1.30v, and the speed of the second particle is unknown. What is the value of n?

hint: In an elastic collision, both the momentum and the kinetic energy of the full system are conserved. Even though the motion in this problem is one dimensional, momentum is still a vector quantity, and the direction (sign) of a particle's velocity is important.

Explanation / Answer

v1f = (m - n m)/(m + n m) (-v) + (2 n m)/(m + n m) (v)

1.3 v = (m - n m)/(m + n m) (-v) + (2 n m)/(m + n m) (v)

==> n = 1.35

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