Ans 1276 Masses A and B, each mass m, are joined by a massless rod of length d,
ID: 1455786 • Letter: A
Question
Ans1276 Masses A and B, each mass m, are joined by a massless rod of length d, and the system lies on a frictionless, horizontal plane Particle c, also of mass m, approaches B with velocity vo along a line perpendicular to AB, and collides with and sticks to B. All masses may be treated as points. Describe the motion of the system after collision- specifically, find the velocity of the Ca of the system of 3 masses, and the angular velocity. Through wha t point does the system have a fixed or instantaneous axis of rotation, if any, after the collision?
Explanation / Answer
initial linear momentum Pi = m*vo
final linear momentum Pf = (m+m+m)*v
from mmentum conservation
Pf =Pi
(m+m+m)*v = m*vo
v = V0/3 <<------answer
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center of mass = m*d/(m+m+m) = d/3 from B
iniital angular momentum Li = m*vo*d/3
I = 2m*(d/3)^2 + m*(2d/3)^2
I = m*d^2*(2/3)
Lf = I*w
final angular momentum Lf = I*w
Lf = Li
(2/3)*m*d^2*w = m*vo*d/3
w = vo/2d <<-----answer