A glider of mass 0.146kg is moving to the right on a frictionless, horizontal ai

Question

A glider of mass 0.146kg is moving to the right on a frictionless, horizontal air track with a speed of 0.840m/s . It has a head-on collision with a glider 0.298kg that is moving to the left with a speed of 2.27m/s . Suppose the collision is elastic.

a)Find the magnitude of the final velocity of the 0.146kg glider.

b)Find the direction of the final velocity of the 0.146kg glider.

c)Find the magnitude of the final velocity of the 0.298kg glider.

d)Find the direction of the final velocity of the 0.298kg glider.

Explanation / Answer

elastic collisions

m1*u1 + m2*u2 = m1*v1+m2*v2

m1*(u1-v1) = m2*(v2-u2)........(1)

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)

u1 = 0.84...........u2 = -2.27

v1 = ?...........v2 = ?

a) v1 = -3.337 m/s

b) left

c) v2 = 0.407 m/s

d) to the right

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