End A of a uniform 10-kg bar is attached to a horizontal rope and end B contacts
ID: 1921057 • Letter: E
Question
End A of a uniform 10-kg bar is attached to a horizontal rope and
end B contacts a floor with negligible friction. Knowing that the
bar is released from rest in the position shown, determine immediately
after release (a) the angular acceleration of the bar, (b) the
tension in the rope, (c) the reaction at B.
rod AB has an angular velocity ?=4 rad/s counter-clockwise and length of the cable attached to A is 2m
End A of a uniform 10 - kg bar is attached to a horizontal rope and end B contacts a floor with negligible friction. Knowing that the bar is released from rest in the position shown, determine immediately after release (a) the angular acceleration of the bar, (b) the tension in the rope, (c) the reaction at B. rod AB has an angular velocity ?=4 rad/s counter - clockwise and length of the cable attached to A is 2mExplanation / Answer
(a)let tension be T
we take moment about B
-Tlsin45+mgl/2sin45=ml^2/3 ?
a=acceleration of center of mass
a=?l/2
l=1
-Tsin45+mg/2 sin45=2ma/3
now equating forces in horizontal direction
T=max
ax=asin45
T=masin45
-ma(sin45)^2+mg/2=2ma/3
a=g/(2*(2/3+1/2))=4.204 m/s^2
g=9.81
T=10*4.204*sin45=29.73 N
let normal reaction be N
equating forces in vertical direction
mg-N=may
ay=acos45
N=m(g-acos45)
=10*(9.81-4.204*cos45)
=68.37 N
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