Lesson_Text_4.4

# Lesson_Text_4.4 - Lesson 18 Equilibrium of Rigid Bodies 1...

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Lesson 18 Equilibrium of Rigid Bodies 1. Conditions of Equilibrium of a rigid Body. An object in equilibrium has: (a) no translational motion (b) no rotational motion In order that there may be no translational motion, the net force acting on the object in the x and y direction should be zero. In order that there may be no rotation, the net torque acting on the object must be zero. In short, conditions of equilibrium for a rigid object can be stated as follows: (i) The sum of all the forces in the x direction should be zero. In other words, Σ F x = 0 …(i) (ii) The sum of all the forces acting in the y direction must be zero. Or, Σ F y = 0 …(ii) (iii) The sum of all the torques acting on the object must be zero. Or, Σ τ = 0 …(iii) In solving problems on equilibrium, it will be useful to follow the following steps. (i) Identify the object or point in equilibrium, draw all the forces acting on it and mark all given distances. (ii) If the forces are not in proper x or y directions, resolve them into x and y components. (iii) Apply the three conditions of equilibrium given above and form equations. (iv) Solve the equations for the unknown

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2. Couple. Two parallel and equal forces acting in the opposite directions on an object such that their points of applications are different is called a couple. Fig.1 below shows the action of a couple on an object. F 1 F 2 d Fig.1 Forces F 1 and F 2 are equal in magnitude but opposite in direction. Their points of applications are separated by a distance d. The function of a couple is to produce rotation. When you open a faucet, it is a couple that does the job. A couple is in action when you use a screwdriver to drive a screw in. The rotation effect of a couple is called the moment (moment is another word for torque) of the couple. The perpendicular distance between the lines of action of the two forces is called the moment arm. In fig. 1, d is the moment arm. The moment of a couple is the product of one of the forces and the moment arm. Example1 : A 35-kg child sits on a uniform seesaw 2.0 m from the pivot point. How far from the pivot point on the other side will her 30-kg playmate has to sit for the seesaw to be in equilibrium. Solution: The figure below shows the three forces acting on the seesaw. To solve this problem we take the torque of these three forces about a perpendicular axis through the pivot point.
2.0 m x 343 N 294 N pivot Fig. 2 The net torque is zero.

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Lesson_Text_4.4 - Lesson 18 Equilibrium of Rigid Bodies 1...

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