Coefficient of friction problem

In summary, if the car is travelling at a speed of μs, and the package is resting on the dashboard, the minimum acceleration that will cause the package to slip off the dashboard is a = 0.333μs.
  • #1
xxpbdudexx
20
0
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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  • #2
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.
 
  • #3
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.)
 
  • #4
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.
 
  • #5


I would approach this problem by first defining the variables and parameters involved. The coefficient of friction, μs, represents the ratio of the force required to overcome the friction between two surfaces (in this case, the package and the dashboard) to the normal force between them. The normal force is the force that the dashboard exerts on the package due to gravity.

Next, I would use the equation μ = F/N to determine the maximum force of friction that can be exerted on the package before it starts to slip. In this case, the maximum force of friction would be μs times the normal force, or μs * mg, where m is the mass of the package and g is the acceleration due to gravity.

To determine the minimum acceleration of the car that would cause the package to slip, we need to consider the forces acting on the package. The only force acting horizontally is the force of friction. Therefore, we can use Newton's second law, F = ma, to determine the minimum acceleration required for the package to slip. Setting F equal to the maximum force of friction, we can solve for a.

So, the minimum acceleration required for the package to slip off the dashboard would be a = μs * g. Plugging in the given value of μs = 0.333 and the standard value of g = 9.8 m/s^2, we get a minimum acceleration of approximately 3.26 m/s^2. This means that the car would need to accelerate at least 3.26 m/s^2 for the package to start slipping off the dashboard.

However, it is important to note that this calculation assumes that the car is on a level road and that the package is not affected by any other external forces. In real-world situations, there may be other factors at play such as air resistance, vibrations, or uneven road surfaces that could affect the minimum acceleration required for the package to slip. Therefore, further analysis and experimentation may be necessary to accurately determine the minimum acceleration in a specific scenario.
 

1. What is the coefficient of friction?

The coefficient of friction is a value that represents the amount of resistance between two surfaces in contact with each other. It is a dimensionless number that ranges from 0 to 1, with 0 indicating no friction and 1 indicating maximum friction.

2. How is the coefficient of friction calculated?

The coefficient of friction is calculated by dividing the force required to move an object over a surface by the weight of the object. This is usually done by using a device called a tribometer which measures the amount of force needed to move an object over a surface.

3. What factors affect the coefficient of friction?

The coefficient of friction is affected by several factors including the nature of the surfaces in contact, the roughness of the surfaces, the amount of force applied, and the presence of lubricants or contaminants between the surfaces.

4. Why is the coefficient of friction important?

The coefficient of friction is important in many applications, such as transportation, manufacturing, and sports. It helps determine the amount of force needed to move objects over different surfaces and is crucial in designing and improving machinery, equipment, and sports equipment.

5. How can the coefficient of friction be reduced?

The coefficient of friction can be reduced by using lubricants, polishing or smoothing the surfaces, and using different materials with lower coefficients of friction. Additionally, increasing the surface area or distributing the weight of an object can also help reduce friction.

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