How Does Particle B's Movement Depend on Particle A's Velocity Direction?

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SUMMARY

The movement of Particle B is directly influenced by the velocity direction of Particle A, which is projected across a smooth horizontal table. When Particle A moves along the line AB, Particle B begins to move immediately as the tension in the string becomes effective. In scenarios where Particle A's velocity is at a 120-degree angle to AB or perpendicular to AB, Particle B starts moving only when the distance between the two particles reaches 2l. The momentum transfer from Particle A to Particle B is calculated using the angle of the string and momentum conservation principles.

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  • Understanding of classical mechanics principles, particularly momentum conservation.
  • Familiarity with vector components and angles in physics.
  • Knowledge of tension in strings and its effects on connected particles.
  • Ability to draw and interpret free body diagrams.
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  • Study the principles of momentum conservation in two-body systems.
  • Learn how to analyze forces in connected particle systems using free body diagrams.
  • Explore the effects of angles on momentum transfer between particles.
  • Investigate the dynamics of tension in strings and its role in particle motion.
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Students of physics, particularly those studying mechanics, educators teaching classical mechanics concepts, and anyone interested in understanding the dynamics of connected particle systems.

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6. Two particles, each of mass m, are connected by a light inextensible string of length 2l. Initially they lie on a smooth horizontal table at points A and B distant l apart. The particle at A is projected across the table with velocity u. Find the speed with which the second particle begins to move if the directions of u is.
(a) along AB,
(b) at an angle of 120 degree with AB,
(c) perpendicular to AB.


How to solve for the b and c part? What`s the usage of the 2 given lengths?
 
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I assume the string is flexible.
For the b part you just imagine or draw atleast a free diagram to get a pictue of what I am saying. The mommentum will slowly betransferred to B. After sometime they will start moving in the same direction and the string becomes straight. The tension starts to act when distance apart become 2l. Proceed from this information.
 
Particle B only starts moveing when the distance between the particles is 2l. Fist figure out the angle between the string and AB when this happens. Since particle B is pulled only by the string, you need to find the component of A's momentum along the string (using the angle) and then calculate how much gets transferred to B using momentum conservation.
 

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