A body of mass 40 kg resting on a rough horizontal surface...

A body of mass $40 \mathrm{~kg}$ resting on a rough horizontal surface is subjected to a force $P$ which is just enough to start the motion of the body. If $\mu_{n}=0.5, \mu_{k}=0.4$, $g=10 \mathrm{~ms}^{-2}$ and the force $P$ is continuously applied on the body, then the acceleration of the body is (a) $2 \mathrm{rro}$ (b) $1 \mathrm{~ms}^{-2}$ (c) $2 \mathrm{~ms}^{-2}$ (d) $2.4 \mathrm{~ms}^{-2}$

A body of mass $40 \mathrm{~kg}$ resting on a rough horizontal surface is subjected to a force $P$ which is just enough to start the motion of the body. If $\mu_{n}=0.5, \mu_{k}=0.4$, $g=10 \mathrm{~ms}^{-2}$ and the force $P$ is continuously applied on the body, then the acceleration of the body is
(a) $2 \mathrm{rro}$
(b) $1 \mathrm{~ms}^{-2}$
(c) $2 \mathrm{~ms}^{-2}$
(d) $2.4 \mathrm{~ms}^{-2}$

Key Concepts

Static Friction

Static friction is the resistive force that prevents an object from starting to move when a force is applied. It acts in opposition to the direction of the intended motion and has a maximum value proportional to the normal force between the surfaces in contact, determined by the coefficient of static friction. This concept is crucial when analyzing the conditions required for an object to overcome resistance and begin motion.

Kinetic Friction

Kinetic friction is the force that opposes the motion of an object once it has started moving. It is typically lower in magnitude than static friction for the same surfaces and depends on the kinetic friction coefficient multiplied by the normal force between the surfaces. This concept explains why the frictional resistance changes once an object transitions from rest to motion.

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 fundamental principle of dynamics is used to determine the acceleration of an object by considering all forces acting on it, including applied forces and friction.

Force Transition from Rest to Motion

The transition from static to kinetic friction is a critical concept in understanding motion on rough surfaces. When an applied force just exceeds the maximum static friction, the object begins to move, and the frictional force immediately drops to the kinetic friction value. Analyzing this change is essential to accurately determine the net force and resultant acceleration of the body.

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