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jontyjashan

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In summary, our teacher had asked us to plot graph of frictional force acting on a given mass kept on an incline vs its angle of inclination. I made a graph where the max frictional force was at angle arctan u(coefficient of friction). The graph of friction at angle less than arctan u was proportional to sinx(angle of inclination) and the graph greater than arctan u was proportional to cosx. Am I right, our teacher had asked us to plot graph of frictional force acting on a given mass kept on an incline vs its angle of inclination.i made a graph where the max frictional force was at angle arctan u(coefficient of friction). The graph

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jontyjashan

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cepheid

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jontyjashan said:

Yeah, that seems right. In the regime where static friction applies and the block remains motionless, friction provides whatever force is required to keep the block from sliding. In other words, the friction force is equal (in magnitude) to the component of the block's weight that is

[tex] F_f = mg\sin\theta [/tex]

where theta is the angle of the incline. But there also is a maximum possible static frictional force:

[tex] F_f \leq \mu_s F_N = \mu_s mg\cos\theta [/tex]

where F

[tex] mg\sin(\theta_{\textrm{max}}) = \mu_s mg\cos(\theta_{\textrm{max}}) [/tex]

[tex] \mu_s = \tan(\theta_{\textrm{max}}) [/tex]

[tex] \theta_{\textrm{max}} = \arctan(\mu_s) [/tex]

So I also agree with you there. Above the maximum inclination angle, we are in the regime of kinetic friction, since the block has begun sliding (the friction force is no longer enough to balance the component of the weight parallel to the incline). In this case, the frictional force becomes:

[tex] F_f = \mu_k F_N = \mu_k mg\cos\theta [/tex]

and now we have cosine-dependence on theta, rather than a sine-dependence. This is significant, because it means that the frictional force actually

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jontyjashan

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The purpose of this graph is to show the relationship between the frictional force and the angle of inclination, which is the angle at which an object is tilted or raised from a horizontal surface. This graph can help determine the amount of friction acting on an object at different inclinations, and how it changes as the angle increases or decreases.

The angle of inclination is directly related to the frictional force acting on an object. As the angle of inclination increases, the frictional force also increases. This is because the object's weight is distributed more perpendicular to the surface, resulting in a stronger normal force, which in turn increases the frictional force.

The shape of this graph can be affected by various factors such as the type of surface the object is on, the weight and material of the object, and the amount of force applied to the object. These factors can alter the frictional force and therefore change the shape of the graph.

The coefficient of friction, which is a measure of the frictional force between two surfaces, can directly affect the slope of this graph. A higher coefficient of friction will result in a steeper slope, indicating a stronger relationship between the angle of inclination and the frictional force.

This graph can be useful in various real-life applications, such as designing ramps and slopes for wheelchair accessibility, determining the optimal angle for a car to climb up a hill, and studying the effects of friction on different surfaces. It can also be used in engineering and construction to ensure the safety and stability of structures.

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