Can you solve the particle sliding on a movable inclinded plane problem

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SUMMARY

The "particle sliding on a movable inclined plane" problem can be effectively solved using Newtonian Mechanics without resorting to Lagrangian methods. By analyzing the system from the frame of the inclined plane and incorporating an inertial force, one can apply Newton's second law to the smaller block. Additionally, considering the center of mass of the system allows for the formulation of a second equation, leading to the determination of the accelerations of both the block and the inclined plane.

PREREQUISITES
  • Newton's Second Law of Motion
  • Concept of inertial and non-inertial frames
  • Understanding of relative acceleration
  • Basic principles of mechanics involving center of mass
NEXT STEPS
  • Study the application of Newton's laws in non-inertial frames
  • Explore the concept of inertial forces in mechanics
  • Learn about relative motion and acceleration in physics
  • Investigate problems involving the center of mass in dynamic systems
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Students and professionals in physics, particularly those focusing on classical mechanics, as well as educators looking for practical examples of Newtonian applications in dynamic systems.

Machinus
Can you solve the "particle sliding on a movable inclinded plane" problem...

...using Newtonian Mechanics?

No Lagrangians.
 
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Work from the frame of the inclined plane and write the second law for the smaller block by adding an inertial force.

Then consider that center of mass of the two doesn't accelerate and write another equation. Solve the two and you get the accelerations.

This is basically working from two different frames in the same problem but works since working in non-inertial frame and adding an inertial force is the same as taking relative accelerations into account and working from an inertail frame. But this is sometimes simpler.

spacetime
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