College Physics Problem. Please show all work. Two objects with masses represent

Question

College Physics Problem. Please show all work.

Two objects with masses represented by m and m2 approach each other on a horizontal frictionless table with the same constant speed, vo, as measured by a laboratory observer. The objects undergo a perfectly elastic collision, and it is observed that after the collision, m2 moves off in a direction opposite its original motion with some constant speed v, and mi is stationary. Determine the following (a) the ratio of the two masses, m1/m2 (b) the ratio of their speeds, vivo

Explanation / Answer

given two objects masses m1 and m2, approaching ewach other with same constant speed of vo

after collision, m2 reverses its direction and moves with speed v where as m1 comes to rest

also, the collision is perfectly elastic

a. initial momentum of the system = (m1 - m2)vo

final momentum of the ssytem = m1*0 + m2*v

from conservation of momentum

m2*v = (m1 - m2)vo

also, for elastic collsiion coefficient of restitution = 1

1 = v/(vo + vo) = v/2vo

hence v = 2vo

hence

m2*2vo = (m1 - m2)vo

2m2 = m1 - m2

3m2 = m1

hence

m1/m2 = 3

b. from previous part

v/vo = 2

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