The uniform 71-lb log is supported by the two cables and used as a battering ram
ID: 1828334 • Letter: T
Question
The uniform 71-lb log is supported by the two cables and used as a battering ram. If the log is released from rest in the position shown, calculate the initial tension induced in each cable immediately after release and the corresponding angular acceleration ? of the cables.
For the anglur acceleration I got 6.4188 rad/s^2 is this correct? If not, please help me calculate the correct number as well as the Ta and Tb in pounds.
Here is a link to the question/diagram and answer format:
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The uniform 71-lb log is supported by the two cables and used as a battering ram. If the log is released from rest in the position shown, calculate the initial tension induced in each cable immediately after release and the corresponding angular acceleration ? of the cables. For the angular acceleration I got 6.4188 rad/s^2 is this correct? If not, please help me calculate the correct number as well as the Ta and Tb in pounds.Explanation / Answer
This is a curvilinear translation problem.
a - Angular acceleration
a_t - Tangential acceleration
a_n - Normal acceleration = 0
Sum forces in the normal direction: Ta + Tb - 71cos22 = 0
Ta + Tb = 71cos22 (eq1)
Sum forces in tangential direction: 71cos68 = (71/32.2)*(a_t) = (71/32.2)*a*1.8 (eq2)
a = (32.2*cos68)/1.8 = 6.701 rad/s^2
Sum moments about the center of gravity: Ta*(cos22)*2.05 - Tb*(cos22)*0.65 = 0 (eq3)
2.05Ta = 0.65Tb
Solve (eq1) and (eq3) for Ta and Tb:
Ta = 15.85 lb
Tb = 49.98 lb
a = 6.701 rad/s^2
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