A particle of mass m moving at vo makes a glancing collision with a particle of

Question

A particle of mass m moving at vo makes a

glancing collision with a particle of mass 2m

initially at rest. After the collision, mass m

moves at half its initial speed at an angle ?

relative to its initial velocity, and mass 2m is

moving at angle ? in the opposite sense. No

external forces acted during the collision.

Was the collision elastic?

A particle of mass m moving at vo makes a glancing collision with a particle of mass 2m initially at rest. After the collision, mass m moves at half its initial speed at an angle ? relative to its initial velocity, and mass 2m is moving at angle ? in the opposite sense. No external forces acted during the collision. Was the collision elastic?

Explanation / Answer

The conservation of total momentum tells us that: (m1)(v1i) + (m2)(v2i) = (m1)(v1f) + (m2)(v2f) and a derived formula from an understanding of kinetic energy gives us: (v1f) + (v1i) = (v2f) + (v2i)* *this is assuming a conservation of kinetic energy, which is what happens in a perfectly elastic collision. so.... (0.400kg)(1.4m/s) + (0.750kg)(0m/s) = (0.400kg)(v1f) + (0.750kg)(v2f) 0.56 = (0.400kg)(v1f) + (0.750kg)(v2f) then rearrange the 2nd formula to get one of the final velocities: v1f = v2f + v2i - v1i v1f = v2f + 0 - 1.4 v1f = v2f -1.4 and plug in! 0.56 = (0.400kg)(v2f - 1.4) + (0.750kg)(v2f) 1.12 = (1.15)(v2f) v2f = 0.9739 m/s

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