A uniform slender rod AB rests on a friction horizontal surface, and a force P of magnitude 0.25 lb is applied at A in a direction perpendicular to the rod. Knowing that the rod weighs 1.75 lb. determine the acceleration of (a) point A, (b) point B.

Question-Answer › Category: Engineering Mechanics › A uniform slender rod AB rests on a friction horizontal surface, and a force P of magnitude 0.25 lb is applied at A in a direction perpendicular to the rod. Knowing that the rod weighs 1.75 lb. determine the acceleration of (a) point A, (b) point B.

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GME asked 1 year ago

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Sazid Ahmad answered 1 year ago

Step: 1

Draw the kinematic diagram of the bar as follows:

Step: 2

Calculate the mass moment of inertia of the rod about its center.

Here, is the weight of the rod, is the acceleration due to gravity and is the length of the rod.
Substitute for , for and for .

Step: 3

Consider the force equilibrium equation:

Substitute , for and for g.

Consider the moment equilibrium condition about point .

Substitute , and for .

Step: 4

(a)
Calculate the acceleration of point A.

Substitute for , for and for .

Therefore, the acceleration of point is .

Step: 5

(b)
Calculate the acceleration of point .

Substitute for , for and for .

Negative sign indicates that deceleration at point B.
Therefore, the acceleration of point is .