The coefficient of friction between a body and the surface...

The coefficient of friction between a body and the surface of an inclined plane at $45^{\circ}$ is $0.5$ if $g=9.8 \mathrm{~m} / \mathrm{s}^{2} .$ The acceleration of the body downwards in $\mathrm{m} / \mathrm{s}^{2}$ is (a) $\frac{4.9}{\sqrt{2}}$ (b) $4.9 \sqrt{2}$ (c) $19.2 \sqrt{2}$ (d) $4.9$

The coefficient of friction between a body and the surface of an inclined plane at $45^{\circ}$ is $0.5$ if $g=9.8 \mathrm{~m} / \mathrm{s}^{2} .$ The acceleration of the body downwards in $\mathrm{m} / \mathrm{s}^{2}$ is
(a) $\frac{4.9}{\sqrt{2}}$
(b) $4.9 \sqrt{2}$
(c) $19.2 \sqrt{2}$
(d) $4.9$

Key Concepts

Inclined Plane Dynamics

An inclined plane is a flat surface tilted at an angle relative to the horizontal. Analyzing motion on an inclined plane involves understanding how gravity's force is divided into components parallel and perpendicular to the plane, influencing both the motion of the object and the normal force it experiences.

Force Decomposition

Force decomposition refers to breaking a force vector into its components along mutually perpendicular directions. In the context of an inclined plane, the gravitational force is decomposed into a component acting along the plane which drives the motion and a perpendicular component which determines the normal force.

Coefficient of Friction

The coefficient of friction is a dimensionless number that represents the ratio between the frictional force resisting motion and the normal force pressing the surfaces together. It is crucial for quantifying the frictional resistance on an inclined plane.

Frictional Force

Frictional force is the resistive force that opposes the motion of an object sliding over a surface. It is calculated by multiplying the coefficient of friction by the normal force on the object. This force plays an important role in determining the net acceleration of the body along the inclined plane.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F=ma). This law is applied on an inclined plane by considering all the forces acting parallel to the surface (such as the component of gravitational force and friction) to determine the acceleration.

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