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# 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-AnswerCategory: Engineering MechanicsA 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.
GME asked 1 year ago

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.

1 Answers
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 .

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