How Does a Speck of Dust Affect the Motion of a Box on an Inclined Ramp?

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SUMMARY

The discussion focuses on a physics problem involving a 100 kg box on a 30° inclined ramp, connected to a hanging mass via a massless rope at a 22° angle. The coefficients of friction are μk = 0.40 and μs = 0.60. The participants successfully calculated the maximum weight of the hanging mass that keeps the box at rest, approximately 88 kg. They also explored the effects of a speck of dust on the hanging mass, leading to instability and requiring the calculation of the box's acceleration at the moment it begins to move.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with forces on inclined planes
  • Knowledge of friction coefficients and their implications
  • Ability to set up and solve equations involving tension and acceleration
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  • Study the effects of friction on inclined planes in detail
  • Learn about free body diagrams and their application in physics problems
  • Explore the concept of torque and its relation to pulleys
  • Investigate the dynamics of systems with multiple masses and forces
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for practical examples of inclined plane problems and tension dynamics.

  • #31
TSny said:
Yes, this gives you another equation to work with. You should be careful with the signs. When the block accelerates up the incline, the pulley will rotate clockwise. So, it is a good idea to take clockwise rotation as the positive direction for torque and angular acceleration.



Think about whether or not the right hand side should be zero.
Nope.. it shouldn't be.. it should be equal to Ma A, not 0
 
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  • #32
Yes. It will be important to distinguish between the acceleration of block A and the acceleration of block B. So, I suggest writing the right side as MAaA. You can use the toolbar to enter superscripts and subscripts.
 
  • #33
Oh, I assumed the two blocks would have the same acceleration as they are all in the same system...

Shouldn't acceleration of A be equal to acceleration of B?
 
  • #34
joemost12 said:
Oh, I assumed the two blocks would have the same acceleration as they are all in the same system...

Shouldn't acceleration of A be equal to acceleration of B?

The two accelerations would be equal if the string on the left side of the pulley (connected to block A) were parallel to the incline. You will need to determine the relationship between aA and aB.
 

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