Two uniform rods, ABC of weight 6 lb and DCE of weight 8 lb, are connected by a pin at C and by two cords BD and BE. The T-shaped assembly rotates in a vertical plane under the combined effect of gravity and of a couple M which is applied to rod ABC. Knowing that at the instant shown the tension in cord BE is 2 lb and the tension in cord BD is 0.5 lb, determine (a) the angular acceleration of the assembly, (b) the couple M. Fig. P16.88

Question-Answer › Category: Engineering Mechanics › Two uniform rods, ABC of weight 6 lb and DCE of weight 8 lb, are connected by a pin at C and by two cords BD and BE. The T-shaped assembly rotates in a vertical plane under the combined effect of gravity and of a couple M which is applied to rod ABC. Knowing that at the instant shown the tension in cord BE is 2 lb and the tension in cord BD is 0.5 lb, determine (a) the angular acceleration of the assembly, (b) the couple M. Fig. P16.88

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GME asked 1 year ago

Two uniform rods, ABC of weight 6 lb and DCE of weight 8 lb, are connected by a pin at C and by two cords BD and BE. The T-shaped assembly rotates in a vertical plane under the combined effect of gravity and of a couple M which is applied to rod ABC. Knowing that at the instant shown the tension in cord BE is 2 lb and the tension in cord BD is 0.5 lb, determine (a) the angular acceleration of the assembly, (b) the couple M.
Fig. P16.88

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Sazid Ahmad answered 1 year ago

Step: 1

7949-16-88P AID: 1825 | 22/11/2013
Calculate the tangential acceleration of rod AC .

Here, radius of rotation of rod AC is , and angular acceleration of assembly is .
Substitute 9 in. for .

Calculate the tangential acceleration of rod DE .

Here, radius of rotation of rod DE is .
Substitute 18 in. for .

Calculate the moment of inertia of rod AC .

Here, mass of rod AC is , and length of rod AC is .
Substitute  for , 6 lb for , 32.2  for g, and 18 in. for .

Calculate the moment of inertia of rod DE .

Here, mass of rod DE is , and length of rod DE is .
Substitute  for , 8 lb for , 32.2  for g, and 24 in. for .

Show the free body diagram of the given system as in Figure (1).
$Z:\01_Solutions_Authoring\Mechanical_Engineering\7949\04_Artwork\7949-16-88P_fig1.jpg$
Show the kinetic diagram of the given system as in Figure (2).
$Z:\01_Solutions_Authoring\Mechanical_Engineering\7949\04_Artwork\7949-16-88P_fig2.jpg$
Take moment about point A.
Since the system of external forces is equivalent to system of effective forces, express the system of external moment as:
…… (1)
Take counterclockwise moment as positive.
From Figure (1), calculate .

Here, couple force applied to rod ABC is M.
From Figure (2), calculate .

In Equation (1), substitute M for , and  for .

Substitute  for , 8 lb for , 32.2  for g,  for , 6 lb for ,  for ,  for ,  for , and  for .

…… (2)
Calculate the angle  between rod DE and cord BD.

Here, distance between point B and C is BC, and distance between point D and C is DC.
Substitute 9 in. for BC, and 12 in. for DC.

Show the free body diagram of rod DE as in Figure (3).
$Z:\01_Solutions_Authoring\Mechanical_Engineering\7949\04_Artwork\7949-16-88P_fig3.jpg$
Show the kinetic diagram of rod DE as in Figure (4).
$Z:\01_Solutions_Authoring\Mechanical_Engineering\7949\04_Artwork\7949-16-88P_fig4.jpg$
a)
Take moment about point C.
Since the system of external forces is equivalent to system of effective forces, express the system of external moments as:
…… (3)
Take counterclockwise moment as positive.
From Figure (3), calculate .

Here, tension force in cord BE is , and tension force in cord BD is .
From Figure (4), calculate .

Substitute  for , and  for  in Equation (3).

Substitute 2 lb for , 0.5 lb for , and  for .

Hence, the angular acceleration of assembly is .
b)
Substitute  for  in Equation (2).

Hence, the magnitude of couple M is .