A horizontal forec F aets on a block of mass m1, which is...

A horizontal forec $F$ aets on a block of mass $m_{1}$, which is placed on a block of mass $m_{2}, m_{2}$ is placed on another block of mass $m_{3}$ which is placed on a smooth horizontal floor. I.ct us now pull the blocks with the forces of magnitudes $18 \mathrm{~N}, 100 \mathrm{~N}$ and $15 \mathrm{~N}$ as shown in the figurc. If the coc[licients of static and kinetic friction betwoen all contact surlaces are $\mu_{x}=0.3$ and $\mu_{k}=0.2$ respeetively, find the (a) friction at each surface, (b) acceleration of the blocks. \Lambdassume, $m_{1}=m_{2}=m_{3}=10 \mathrm{~kg}$

A horizontal forec $F$ aets on a block of mass $m_{1}$, which is placed on a block of mass $m_{2}, m_{2}$ is placed on another block of mass $m_{3}$ which is placed on a smooth horizontal floor. I.ct us now pull the blocks with the forces of magnitudes $18 \mathrm{~N}, 100 \mathrm{~N}$ and $15 \mathrm{~N}$ as shown in the figurc. If the coc[licients of static and kinetic friction betwoen all contact surlaces are $\mu_{x}=0.3$ and $\mu_{k}=0.2$ respeetively, find the
(a) friction at each surface,
(b) acceleration of the blocks. \Lambdassume, $m_{1}=m_{2}=m_{3}=10 \mathrm{~kg}$

Key Concepts

Newton's Second Law

This principle states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). In problems involving multiple blocks, Newton's second law is applied to each block or to the entire system to determine the resulting acceleration and how forces such as friction affect the motion.

Static Friction

Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It has an upper limit determined by the coefficient of static friction multiplied by the normal force. Understanding static friction is crucial for determining whether the applied forces are sufficient to overcome this resistance, and if so, when the objects will begin to move relative to each other.

Kinetic Friction

Once the objects begin to slide relative to each other, kinetic friction comes into play. It is generally characterized by a lower coefficient than static friction and is calculated as the product of the coefficient of kinetic friction and the normal force. Kinetic friction affects the acceleration of the objects once slipping has begun, and knowing its value is important for predicting the subsequent motion.

Free Body Diagrams

Free body diagrams are schematic representations that isolate a body and illustrate all external forces acting on it. In problems with multiple blocks, drawing free body diagrams for each block helps in visualizing how forces such as applied forces, normal forces, and friction forces interact, and is essential for setting up the fundamental equations governing the system’s behavior.

Multi-Body Dynamics

In systems where multiple bodies interact, such as stacked blocks, it is important to analyze how forces are transmitted through the system and how friction at each interface affects motion. Multi-body dynamics involves considering both the collective motion of the entire system and the possibility of relative motion between individual components, which is essential for accurately determining accelerations and interfacial friction forces.

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