Stability of bodies in equilibrium — A/L Combined Mathematics

How do I practise Stability of bodies in equilibrium?

1 question with a worked solution

Check before you answer: Potential Energy Formulation: Formulating the total potential energy V(θ) as a function of the angular displacement θ with respect to a fixed datum.

1. A rigid body resting in equilibrium on a horizontal surface is in stable equilibrium if, upon a slight displacement from its equilibrium position:
   1. A) Its center of gravity rises and the resulting forces generate a restoring moment returning it to equilibrium
   2. B) Its mass increases instantaneously
   3. C) Its center of gravity lowers and the resulting moment tips it further away
   4. D) Its center of gravity remains at the exact same height without any moment
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   Correct answer: A) Its center of gravity rises and the resulting forces generate a restoring moment returning it to equilibrium

   In stable equilibrium, potential energy is at a local minimum. When slightly disturbed, the center of gravity rises (increasing PE), and the lines of action of the weight and reaction form a couple that creates a restoring moment, bringing the body back to its original equilibrium position.

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   Step 1: Stable equilibrium condition: Local minimum potential energy. Step 2: Disturbance raises CG and generates restoring moment. Answer: Its center of gravity rises and the resulting forces generate a restoring moment returning it to equilibrium.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Stability of bodies in equilibrium fit in the syllabus?

Year 2 · Term 2