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Let two objects of equal mass m collide
Let two objects of equal mass m collide. Object 1 has initial velocity v. directed to the right, and object 2 is initially stationary. If the colliston is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2? Give the velocity v1 of object 1 followed by the velocity v2 of object 2. separated by a comma. Express each velocity in terms of v. Now suppose that the collision is perfectly inelastic What are the velocities Wj and Vj of the two objects after the collision? Give the velocity V1 of object 1 followed by the velocity V2 of object 2. separated by a comma. Express the velocities in terms of V. Now assume that the mass of object 1 is 2m.
Expert Solution
according to conservation of linear momentum
m1*u1 + m2*u2 = m1*v1+m2*v2
m1*(u1-v1) = m2*(v2-u2)........(1)
according to conservation of energy
0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2
m1*(u1^2 - v1^2) = m2*(v2^2-u2^2).....(2)
from 1 &2
u1 + v1 = u2+v2
u1 - u2 = v2 - v1
v2 = u1 - u2 + v1........(3)
3 in 1
m1*(u1-v1) = m2*(u1 - u2 + v1 - u2)
v1 = u1*(m1-m2)/(m1+m2) + 2*m2*u2/(m1+m2)
v2 = u2*(m2-m1)/(m1+m2) + 2*m1*u1/(m1+m2)
0 ,v
part B
V1 = v2 = mv/(m+m) = v/2 , v/2
partC
v/3 , 4v/3
part D
-3v/4 , v/2
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