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Questions and Answers
What does D'Alembert's Principle state?
What does D'Alembert's Principle state?
- The sum of the forces on a particle is equal to the inertial force
- The sum of the forces acting on a particle and its mass multiplied by acceleration is zero
- The sum of the forces acting on a particle equals its mass times velocity
- The sum of the forces acting on a particle and twice the mass of that particle, multiplied by its acceleration, is equivalent to zero (correct)
How is the inertial force represented in D'Alembert's Principle?
How is the inertial force represented in D'Alembert's Principle?
- Mass times jerk
- Mass divided by acceleration
- Twice the acceleration divided by mass
- Twice the mass times acceleration (correct)
What purpose does the inertial force serve in D'Alembert's Principle?
What purpose does the inertial force serve in D'Alembert's Principle?
- To make the particle move with constant velocity
- To increase the mass of the particle
- To account for the effects of acceleration in a non-inertial frame (correct)
- To balance the applied forces on the particle
In what situations is D'Alembert's Principle applicable?
In what situations is D'Alembert's Principle applicable?
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How does D'Alembert's Principle simplify dynamic analysis problems?
How does D'Alembert's Principle simplify dynamic analysis problems?
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What role does the application of D'Alembert's Principle play in formulating equations of motion?
What role does the application of D'Alembert's Principle play in formulating equations of motion?
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Study Notes
D'Alembert's Principle
- Named after French mathematician and physicist Jean le Rond d'Alembert
- Fundamental concept in classical mechanics, primarily used in Newtonian mechanics
- Special case of the more general principle of virtual work
Mathematical Expression
- F + m x a = 0
- Where: F is the vector sum of all forces acting on the particle
- m is the mass of the particle
- a is the acceleration of the particle
Key Concept
- Asserts that for a particle in equilibrium or uniform rectilinear motion, the algebraic sum of applied forces and inertial force (twice the mass times acceleration) is zero
Inertial Force
- m·a, a pseudo-force introduced to account for acceleration effects in a non-inertial reference frame
- Allows analysis of dynamic systems as if they were in equilibrium
Applications
- Useful in formulating equations of motion and dynamic analysis problems
- Simplifies analysis by transforming dynamic problems into static ones, making it easier to apply principles of static equilibrium
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