Coefficient of friction problem

AI Thread Summary
The problem involves determining the minimum acceleration of a car required for a package to slip off its dashboard, given a coefficient of static friction (μs = 0.333). To solve it, one must analyze the forces acting on the package, including horizontal and vertical forces, and apply the equation ma = mgμ, where m is the mass of the package and a is the car's acceleration. The solution reveals that the mass cancels out, simplifying the calculation. Ultimately, the acceleration can be derived from the relationship between the forces and the coefficient of 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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