Will a block slide in a moving lift with equilibrium?

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Homework Help Overview

The discussion revolves around the dynamics of a block in a moving lift, specifically examining the conditions under which the block may slide. The subject area includes concepts from mechanics, particularly forces, friction, and acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between effective gravity and the conditions for sliding, with some questioning the implications of their equations. There is exploration of scenarios involving different gravitational accelerations, such as on the Moon.

Discussion Status

Participants are actively engaging with the problem, questioning their assumptions and interpretations. Some guidance has been offered regarding the relationship between static friction and gravitational acceleration, but no consensus has been reached on the overall understanding of the situation.

Contextual Notes

There is mention of the block's behavior under different conditions of the lift, including rest and constant velocity, as well as the implications of varying gravitational forces. The discussion reflects uncertainty regarding the application of static friction in these scenarios.

ProfManas
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Homework Statement



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Homework Equations



The Attempt at a Solution


[/B]
Effective gravity = g-a
So
Frictional force = tension
Tension = m(g-a)
u 2m(g-a) =m(g-a)
 

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Hi ProfManas and welcome to PF.

So what is your answer? Your equations appear to be correct.
 
kuruman said:
Hi ProfManas and welcome to PF.

So what is your answer? Your equations appear to be correct.
Answer through equations is g=a which feels wrong.
I think maybe lift can descend with whatever deceleration less than g and the equilibrium will still hold? I m stumped.
 
ProfManas said:
Answer through equations is g=a which feels wrong.
It feels wrong but it isn't. There is an important lesson to be learned here.

If the lift were at rest or moving at constant velocity, the block would not slide because μs(2mg) > mg. Would it slide on the Moon where the acceleration of gravity is about 1/6 of 9.8 m/s2? No. That's because both the tension and the maximum force of static friction scale as whatever value the acceleration of gravity has. If the acceleration of gravity is reduced by a factor of 1/6, so is the maximum force of static friction and the inequality is preserved. Conversely, if the block does slide when the acceleration of the lift is zero, then it will also slide when the lift is accelerating up or down, it doesn't matter.
 
kuruman said:
It feels wrong but it isn't. There is an important lesson to be learned here.

If the lift were at rest or moving at constant velocity, the block would not slide because μs(2mg) > mg. Would it slide on the Moon where the acceleration of gravity is about 1/6 of 9.8 m/s2? No. That's because both the tension and the maximum force of static friction scale as whatever value the acceleration of gravity has. If the acceleration of gravity is reduced by a factor of 1/6, so is the maximum force of static friction and the inequality is preserved. Conversely, if the block does slide when the acceleration of the lift is zero, then it will also slide when the lift is accelerating up or down, it doesn't matter.
That does make sense, thanks.
 

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