Acceleration Incline With Stationary Mass

In summary, the problem involves a block resting on an inclined wedge, with a horizontal force acting on the wedge. The coefficient of static friction between the block and wedge is given, along with the angle of the incline. The goal is to determine the maximum and minimum values of the horizontal force to prevent the block from slipping. The equations needed for solving the problem are the relationship between static friction and normal force, and the net force equation. However, the specific steps for finding the values of F are unclear.
  • #1
kneu
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Homework Statement



Given: A block of mass 0.30 kg rests on the inclined surface of a wedge of mass 1.0 kg. The wedge is acted on by a horizontal force and slides on a frictionless surface.

Question: If the coefficient of static friction between the wedge and the block is µs = 0.40, and the angle of the incline is 35°, find the maximum and minimum values of F for which the block does not slip.

Homework Equations



µ_s(F_n) = F_f

F_net = ma

The Attempt at a Solution



Unsure how to begin.
 
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  • #2
I understand that the normal force is equal to the weight of the wedge, mg. I'm not sure how to use the friction coefficient and angle of inclination to determine the maximum and minimum values of F.
 

What is acceleration incline with stationary mass?

Acceleration incline with stationary mass refers to the phenomenon where a mass remains stationary on an incline despite the presence of an external force, such as gravity. This occurs when the force of gravity is balanced by an equal and opposite force, known as the normal force, exerted by the incline.

What factors affect acceleration incline with stationary mass?

The main factors that affect acceleration incline with stationary mass are the angle of the incline, the coefficient of friction between the mass and the incline, and the mass of the object. A steeper incline or a higher coefficient of friction will result in a greater normal force and therefore a larger tendency for the mass to remain stationary. Conversely, a lighter mass or a lower coefficient of friction will result in a smaller normal force and a greater tendency for the mass to slide down the incline.

How is acceleration calculated for a stationary mass on an incline?

The acceleration of a stationary mass on an incline can be calculated using Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the difference between the force of gravity and the normal force, and the acceleration is the acceleration due to gravity. Therefore, the equation for acceleration on an incline is a = (mgsinθ - μmgcosθ)/m, where m is the mass of the object, g is the acceleration due to gravity, θ is the angle of the incline, and μ is the coefficient of friction.

How does the angle of the incline affect acceleration incline with stationary mass?

The angle of the incline has a significant impact on acceleration incline with stationary mass. As the angle increases, the component of the force of gravity acting down the incline also increases, resulting in a larger normal force and a greater tendency for the mass to remain stationary. This means that a higher incline angle will result in a lower acceleration for the stationary mass.

What is the role of friction in acceleration incline with stationary mass?

Friction plays a crucial role in acceleration incline with stationary mass. Without friction, the mass would simply slide down the incline due to the force of gravity. However, the presence of friction between the mass and the incline creates a normal force that balances out the force of gravity and prevents the mass from sliding. The coefficient of friction determines the strength of this force, and a higher coefficient of friction will result in a larger normal force and therefore a greater tendency for the mass to remain stationary.

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