A block of mass m sits on the top of an identical block...

A block of mass $m$ sits on the top of an identical block which sits on the top of a flat rough table. 'The coefficient of static friction between the surfaces of the blocks is $\mu_{1}$ and coefficient of static friction between the block and table is $\mu_{2}$. If $m=5 \mathrm{~kg} ; \mu_{1}=0.6$ and $\mu_{3}=0.2$. 'lhen the minimum force to be applied on the top block to produce motion in the system of blocks is (take $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (a) $20 \mathrm{~N}$ (b) $17.14 \mathrm{~N}$ (c) $19.61 \mathrm{~N}$ (d) $51.44 \mathrm{~N}$

A block of mass $m$ sits on the top of an identical block which sits on the top of a flat rough table. 'The coefficient of static friction between the surfaces of the blocks is $\mu_{1}$ and coefficient of static friction between the block and table is $\mu_{2}$.
If $m=5 \mathrm{~kg} ; \mu_{1}=0.6$ and $\mu_{3}=0.2$. 'lhen the minimum force to be applied on the top block to produce motion in the system of blocks is (take $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $20 \mathrm{~N}$
(b) $17.14 \mathrm{~N}$
(c) $19.61 \mathrm{~N}$
(d) $51.44 \mathrm{~N}$

Key Concepts

Force Equilibrium and Threshold of Motion

Force equilibrium occurs when all forces acting on an object balance out, resulting in no net movement. For motion to start, an applied force must exceed the sum of resistive forces, such as static friction, that maintain equilibrium. Analyzing this balance helps determine the minimum force required to initiate motion in a system.

Interface Analysis in Multi-Body Systems

In systems involving several contacting surfaces, such as stacked blocks, it is important to analyze each interface separately. The interface with the lowest maximum static friction force (determined by its coefficient and the corresponding normal force) typically governs when the overall system will begin to move, requiring careful consideration of how forces are distributed between the objects.

Static Friction

Static friction is the force that prevents two surfaces in contact from sliding relative to each other until a certain threshold is reached. It is characterized by the maximum force available before motion begins, which is calculated by multiplying the coefficient of static friction by the normal force between the surfaces.

Normal Force

The normal force is the perpendicular force exerted by a surface that supports an object resting on it. In friction problems, this force is crucial because it directly influences the maximum static friction available at any interface and is typically determined by the weight of the object or objects in contact.

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