Finding acceleration on an incline plane with static friction

• Arclite Cham
In summary, the person is having trouble with a physics question involving the static friction between two objects. They are asking for help in determining the reaction force between the two objects and how it affects the total acceleration. They have attempted to solve the problem by assuming the weight of one object and considering the force to be horizontal, but have encountered an error. They are advised to draw free-body diagrams and consider both scenarios of slipping and not slipping.
Arclite Cham
Hello everyone I am a newbie as well as in physics. I am having a problem in a question as in the attachment. I have learned that the equation of the static friction (Fs) of an object is equals to the product of the coefficient to the normal force of the object.

In this question, let mass of A be M(a) and mass of B be M(b) and the total mass of A and B be M.
Assume g is the gravitational acceleration with 9.81ms^-2.

However, in this question, what is the reaction force for the Fs between A and B? Is it M times cos θ or just 0.4gM(a)? And after finding the Fs, how does it affect the total acceleration of the objects? Does the kinetic friction have anything to do with the result? I tried to find the Fs by assuming the weight of A times 0.4. Then I consider the force to be horizontal to the plane and hence the force opposing the motion (Fb) would be Fs cos θ. After that the resultant force will equals to Mg sin θ - Fb. But that gave me a negative answer. So where is the error?

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Hello, Arclite Cham. Welcome to PF.

This is one of those problems where you don't know ahead of time whether there's enough static friction to prevent A from slipping on B. One approach is to assume there is no slipping and then calculate under this assumption what the normal force and friction force would be between A and B. You will then be able to see if the coefficient of static friction given in the problem is sufficient to provide the necessary friction force. If so, then the problem is essentially solved. If not, you will have to then assume that A slips on B and re-do the analysis for slipping.

In any case, you're going to need carefully drawn free-body diagrams for A and B so that you can apply Newton's laws to each body.

1. What is static friction on an incline plane?

Static friction is the resistance force that occurs between two surfaces that are in contact with each other and are not moving relative to each other. On an incline plane, static friction acts to prevent an object from sliding down the ramp.

2. How is acceleration calculated on an incline plane with static friction?

The formula for calculating acceleration on an incline plane with static friction is a = g(sinθ - μcosθ), where a is the acceleration, g is the gravitational acceleration (9.8 m/s²), θ is the angle of the incline, and μ is the coefficient of static friction between the object and the incline plane.

3. What factors affect the magnitude of static friction on an incline plane?

The magnitude of static friction on an incline plane is affected by the coefficient of static friction between the object and the incline plane, the weight of the object, and the angle of the incline. As the angle of the incline increases, the magnitude of static friction also increases.

4. Can an object ever accelerate on an incline plane with static friction?

Yes, an object can accelerate on an incline plane with static friction if the force pushing or pulling the object is greater than the force of static friction. This is known as the maximum static friction force, and once it is exceeded, the object will begin to accelerate down the incline.

5. How does the direction of static friction change on an incline plane?

The direction of static friction acts parallel to the incline plane and in the opposite direction of the movement that the object would make if it were to slide down the incline. As the angle of the incline increases, the direction of static friction also changes to oppose the increasing angle.

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