Question

A 0.385-kg blue bead slides on a frictionless, curved wire, starting from rest at point circled A in the figure below, where h = 1.50 m. At point circled B, the blue bead collides elastically with a 0.585-kg green bead at rest. Find the maximum height the green bead rises as it moves up the wire.

Answer 1

for blue u1 = sqrt(2*g*h) = 5.42 m/s

for elastic collisions

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)

m1(blue) = 0.385 kg.....m2(green) = 0.585 kg

u1 = 5.42...........u2 = 0

v1 = (5.42*(.385-.585))/(.385+.585) = -1.12 m/s

v2 ( green) = (2*.385*5.42)/(.385+0.585) = 4.3 m/s

h = v2^2/2g = (4.3*4.3)/(2*9.8) = 0.943 m