Coefficient of friction problem

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SUMMARY

The problem involves determining the minimum acceleration of a car required to cause a package to slip off its dashboard, given a coefficient of static friction (μs) of 0.333. The key equation derived from the discussion is ma = mgμ, where 'm' is the mass of the package, 'a' is the car's acceleration, and 'g' is the acceleration due to gravity. The solution confirms that the mass cancels out, simplifying the calculation to a direct relationship between acceleration and the coefficient of friction.

PREREQUISITES
  • Understanding of static friction and its coefficient (μs)
  • Basic knowledge of Newton's second law (F = ma)
  • Familiarity with free body diagrams
  • Concept of gravitational force (F = mg)
NEXT STEPS
  • Explore the implications of varying coefficients of friction in different materials
  • Learn about free body diagram techniques for analyzing forces in physics problems
  • Study the effects of acceleration on objects in non-inertial reference frames
  • Investigate real-world applications of static friction in automotive safety
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as engineers and automotive designers interested in vehicle dynamics and safety features.

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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