A block is kept over a rough horizontal ground with...

A block is kept over a rough horizontal ground with coefficient of friction $\mu . \Lambda \mathrm{t}$ the instant shown, block is at rest. Take this moment as $t=0$ $\Lambda$ t this moment, a time dependent force oiven by $F=F_{0} e^{-t / \tau}$ starts acting on the block along horizontal. Here, $\tau$ and $F_{0}$ are known constants. The mass of the block is $m$. The minimum value of $F_{n}$ so that the block starts slipping over the surface is (a) $>\mu \mathrm{mg}$ (b) $>\frac{\mu m g}{\sqrt{1+\mu^{2}}}$ (c) $>\left(\sqrt{1+\mu^{2}}\right) m g$ (d) $\frac{m g}{\mu}$

A block is kept over a rough horizontal ground with coefficient of friction $\mu . \Lambda \mathrm{t}$ the instant shown, block is at rest. Take this moment as $t=0$ $\Lambda$ t this moment, a time dependent force oiven by $F=F_{0} e^{-t / \tau}$ starts acting on the block along horizontal. Here, $\tau$ and $F_{0}$ are known constants. The mass of the block is $m$.
The minimum value of $F_{n}$ so that the block starts slipping over the surface is
(a) $>\mu \mathrm{mg}$
(b) $>\frac{\mu m g}{\sqrt{1+\mu^{2}}}$
(c) $>\left(\sqrt{1+\mu^{2}}\right) m g$
(d) $\frac{m g}{\mu}$

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Key Concepts

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It adjusts in magnitude up to a maximum limit, which is determined by the normal force and the coefficient of static friction, to keep the object at rest under applied forces.

Coefficient of Friction

The coefficient of friction is a dimensionless value that characterizes the interaction between two surfaces. It determines the maximum frictional force available, as it multiplies the normal force to yield the maximum static friction force before sliding begins.

Normal Reaction Force

The normal reaction force is the perpendicular force exerted by a surface to support the weight of an object resting on it. It is crucial in friction problems as it directly influences the frictional force available between the object and the surface.

Time-Dependent Forces

Time-dependent forces are forces whose magnitude (and possibly direction) changes over time. Analyzing such forces requires understanding not only the instantaneous conditions for motion but also how changing forces may affect the transition from static equilibrium to motion.

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