Analyzing Mass A's Direction of Motion

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SUMMARY

The discussion focuses on analyzing the direction of motion for mass A in a system involving two masses on an inclined plane, specifically a 50 kg mass (B) and a 10 kg mass (A). The participants emphasize the importance of understanding the forces at play, including tension and friction, and how they affect the motion of the masses. Key equations derived include the tension forces, T_b = 245.3 N and T_a = 49.05 N, which illustrate that mass B descends while mass A ascends. The analysis concludes that the direction of motion can be inferred from the frictionless case, and the ambiguity in the problem statement regarding the time for A to slide 0.5 m is noted.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of inclined plane dynamics
  • Familiarity with free body diagrams (FBD)
  • Basic concepts of friction and tension in mechanical systems
NEXT STEPS
  • Study the dynamics of inclined planes with multiple masses
  • Learn about free body diagram (FBD) analysis for complex systems
  • Explore the effects of friction on motion in mechanical systems
  • Investigate the principles of Atwood machines and their variants
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of systems involving multiple masses and inclined planes.

  • #31
Another way to get the initial direction is to consider the height of the system's centre-of-gravity (CoG).

When released from rest, the CoG must move downwards, converting gravitational potential energy to kinetic energy (and to heat).

This happens when the height of the heavier object (B) decreases and the height of the lighter object (A) increases.

(If the CoG moved upwards, this would violate the conservation of energy: gravitational potential energy, kinetic energy and heat would need to be created out of nowwhere.)
 
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  • #32
Orodruin said:
There is also friction between the blocks. This of course represents a 3rd law pair but once you straighten the string they act in the same direction because one is turned 180 degrees.
Yes, of course, this makes much more sense. I assumed without thinking that the frictions would cancel like the tensions although it didn't sit well with me because of what happens when the incline is frictionless but there is friction between blocks. My excuse of the day is that my wife was pressuring me to do something for her so I posted in a hurry.
 
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  • #33
kuruman said:
My excuse of the day is that my wife was pressuring me to do something for her so I posted in a hurry.
Add to end of post:
"This post is dedicated to my dear beloved wife."
:wink:
 
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