For the equilibrium of a body on an inclined plane of inclination 45^∘, the coefficient of stati

step 1 in this problem drawing the diagram first so just look at it carefully after that I will simplif

For the equilibrium of a body on an inclined plane of...

Key Concepts

Equilibrium on an Inclined Plane

This concept refers to the condition in which a body on an inclined surface remains at rest because the net force acting on it is zero. In analyzing such situations, the gravitational force is resolved into components parallel and perpendicular to the surface, and the equilibrium condition ensures that the force down the plane is exactly balanced by the frictional force opposing motion.

Force Resolution

Force resolution is the process of decomposing a force into components along specified directions, typically parallel and perpendicular to an inclined plane. This technique is crucial in mechanics because it allows one to apply Newton's laws independently along each axis, facilitating the analysis of equilibrium or motion on an incline.

Coefficient of Static Friction

The coefficient of static friction is a dimensionless number that represents the ratio between the maximum static frictional force that a surface can exert and the normal force pressing the surfaces together. It is a measure of the amount of frictional resistance present and plays a key role in determining whether an object on an incline will remain at rest or begin to slide.

Limiting Equilibrium Condition

The limiting equilibrium condition occurs when the static frictional force reaches its maximum possible value, and any slight increase in the applied force would result in the onset of motion. In this state, the coefficient of static friction is exactly equal to the tangent of the angle of the incline, representing the threshold at which equilibrium is maintained.

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