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Analyzing Equilibrium Problems

Analyzing Equilibrium Problems. Recall the definition of equilibrium: No acceleration Constant Velocity OR Zero Velocity Recall Newton’s Second Law: ∑ F = ∑ m∙ a If acceleration is zero… ∑ F = 0 N. This works in alllll directions! ∑ F x = 0 N ∑ F Y = 0 N

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Analyzing Equilibrium Problems

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  1. Analyzing Equilibrium Problems • Recall the definition of equilibrium: • No acceleration • Constant Velocity OR • Zero Velocity • Recall Newton’s Second Law: • ∑F = ∑m∙a • If acceleration is zero… • ∑F = 0 N • This works in alllll directions! • ∑Fx = 0 N • ∑FY = 0 N • This special case of Newton’s Second Law is the basis for analyzing objects in equilibrium

  2. Equilibrium: Example 1 • In a circus balancing act, a woman performs a headstand on top of a man’s head. The woman weighs 490N. The man’s head and neck weigh 50N. Typically, the humanoid’s seventh cervical vertebra supports all weight above the shoulders. What is the normal force that this vertebra exerts on the neck and head of the man: • Before the act? • During the act?

  3. Equilibrium: Example 2 An automobile engine has a weight W, whose magnitude is 3150 N. Michael the mechanic is using a rope and ring system as shown in the illustration to position the engine. The engine is not moving. (a = 0) There are two ropes in the system, and they are subjected to tensions T1 and T2 as shown. Determine the magnitude of the tension in each rope. (T1 and T2)

  4. Equilibrium: Example 2Continued To determine the magnitude of the tension in each rope start with Newton’s Second Law: • x-direction ∑Fx= 0 N • y-direction ∑Fy = 0 N

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