A wooden box of mass 8 kg slides down an inclined plane of...

A wooden box of mass $8 \mathrm{~kg}$ slides down an inclined plane of inclination $30^{\circ}$ to the horizontal with a constant acceleration of $0.4 \mathrm{~ms}^{-2}$. What is the force of friction between the box and inclined plane? $\left(g=10 \mathrm{~ms}^{-2}\right)$ (a) $36.8 \mathrm{~N}$ (b) $76.8 \mathrm{~N}$ (c) $65.6 \mathrm{~N}$ (d) $97.8 \mathrm{~N}$

A wooden box of mass $8 \mathrm{~kg}$ slides down an inclined plane of inclination $30^{\circ}$ to the horizontal with a constant acceleration of $0.4 \mathrm{~ms}^{-2}$. What is the force of friction between the box and inclined plane? $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $36.8 \mathrm{~N}$
(b) $76.8 \mathrm{~N}$
(c) $65.6 \mathrm{~N}$
(d) $97.8 \mathrm{~N}$

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Key Concepts

Motion on an Inclined Plane

Understanding motion on an inclined plane involves analyzing how gravitational forces, friction, and the plane's angle interact to influence the acceleration of the object. This concept is essential for solving problems where objects slide along slopes under the influence of various forces.

Frictional Force

Friction is the resistive force that opposes the relative motion between two surfaces in contact. On an inclined plane, friction acts opposite to the direction of motion and its magnitude can be determined by comparing the gravitational force component along the plane with the net force needed to produce the observed acceleration.

Newton’s Second Law

Newton’s Second Law states that the net force acting on an object is equal to the mass of that object multiplied by its acceleration. This law is fundamental in analyzing motion and forces, allowing us to relate acceleration to the forces acting along an inclined plane.

Gravitational Force Component

When an object is placed on an inclined plane, gravity can be resolved into two components: one perpendicular to the plane and one parallel to it. The parallel component, calculated as mg sin?, is the force that causes the object to accelerate down the plane.

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