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Ans 1276 Masses A and B, each mass m, are joined by a massless rod of length d,

ID: 1455786 • Letter: A

Question

Ans
1276 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


+++++++++++++++++

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