Coefficient of friction problem

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Homework Help Overview

The problem involves determining the minimum acceleration of a car required to cause a package resting on its dashboard to slip off, given a static friction coefficient. The context is within the subject area of dynamics and friction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relevance of free body diagrams and the forces acting on the package. There is an emphasis on understanding the relationship between the horizontal and vertical forces and the coefficient of static friction.

Discussion Status

Some participants have offered guidance on analyzing the forces involved, while others have reiterated the problem statement and expressed uncertainty about the necessary equations. There appears to be an ongoing exploration of the problem without a definitive consensus on the approach.

Contextual Notes

Participants note that the mass of the package is assumed to be variable, and there is a focus on the conditions under which the package will slip, specifically in relation to the forces and the coefficient of static friction.

xxpbdudexx
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Here is the problem:
"A small package rests on the horizontal dashboard of a car. If μs = 0.333, what is the minimum acceleration of the car that will cause the package to slip off, assuming that the car is on a level road?"

I really have no clue. Any equations I feel are relevant (μ =F/N,standard kinematics equations) require far more information than I have.

Help please?
 
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Try drawing a free body diagram and looking at the forces that are involved 1st. There are probably several ways to look at it, but this essentially would boil down to a box on a moving ramp problem.
 
xxpbdudexx said:
Here is the problem:
"A small package rests on the horizontal dashboard of a car. If μs = 0.333, what is the minimum acceleration of the car that will cause the package to slip off, assuming that the car is on a level road?"

I really have no clue. Any equations I feel are relevant (μ =F/N,standard kinematics equations) require far more information than I have.

Help please?

Assume that the mass of the package is m, and the acceleration of the car is a.
Assuming that the package doesn't slip, in terms of m and a (and g), what are the horizontal and vertical forces acting on the package?

The package will slip only if the calculated horizontal force is greater or equal to the vertical force times the coefficient of static friction. (The mass should cancel out of your final equation.)
 
Chestermiller said:
Assume that the mass of the package is m, and the acceleration of the car is a.
Assuming that the package doesn't slip, in terms of m and a (and g), what are the horizontal and vertical forces acting on the package?

The package will slip only if the calculated horizontal force is greater or equal to the vertical force times the coefficient of static friction. (The mass should cancel out of your final equation.)

Alright, I did this and found out ma = mgμ, and then subsequently solved it. Thanks.
 

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