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Lesson 4.4 Conditions of Equilibrium

# Lesson 4.4 Conditions of Equilibrium - Equilibrium of Rigid...

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Equilibrium of Rigid Bodies Equilibrium is a state of balance. In order that an object may be in equilibrium, all the forces acting on it must be balanced. F net = 0 This can be summarized as: F y = 0 F x = 0 F z = 0 Consider two equal and opposite forces F acting on the object on the right. These forces are balanced because But the object is not in equilibrium because these forces produce a net torque on the object. Another necessary condition for equilibrium is τ net = 0 F F τ = 0 1

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We call this a counterclockwise torque. We call this a clockwise torque. For convenience we take a counterclockwise torque as positive and a clockwise torque as negative. B C A Axis of rotation. This should be zero for rotational equilibrium. 2
Torque of a couple A couple is formed by two equal and opposite parallel forces on an object so that their points of applications are different We find the torque of these forces about an axis through A Now we take the torque of these two forces about B F 2 B C A F 1 Torque of a couple is the product of one of the forces and the perpendicular distance between the forces . = BA·F1 = AB·F 2 (F 1 = F 2 in magnitude) 3

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Solving problems using equilibrium conditions To solve problems using conditions of equilibrium, we use the following steps: 1. Identify the point or object in equilibrium 2. Draw vectors to represent all the forces acting on the object 3. Resolve the force vectors into x- and y-components 4. Mark all the distances 6. Find the torque of all the forces about any chosen axis 7. Use τ = 0 to form another equation. 8. Solve the equations for the unknown. 4
A uniform meter stick pivoted at its center has a mass 100 g suspended at the 25 cm position. (a) At what position should a 75.0 g mass be suspended to put the system in equilibrium? (b) What mass would have to be suspended at the 90 cm mark for the system to be in equilibrium? (a)

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Lesson 4.4 Conditions of Equilibrium - Equilibrium of Rigid...

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