A, Block B In Fig. 3-41 a, a constant horizontal force F⃗a is applied to block A, which pushes a

step 1 This problem covers the concept of Newton's second law of motion. And in the first case, the for

A, Block B In Fig. 3-41 a, a constant horizontal force F⃗a...

A, Block $B$ In Fig. $3-41 a$, a constant horizontal force $\vec{F}_{a}$ is applied to block $A$, which pushes against block $B$ with a $20.0 \mathrm{~N}$ force horizontally to the right. In Fig. $3-41 b$, the same force $\vec{F}_{a}$ is applied to block $B ;$ now block $A$ pushes on block $B$ with a $10.0 \mathrm{~N}$ force horizontally to the left. The blocks have a total mass of $12.0 \mathrm{~kg}$. What are the magnitudes of (a) their acceleration in Fig. $3-41 a$ and (b) force $\vec{F}_{a} ?$

Key Concepts

Free-Body Diagrams

A free-body diagram is a schematic representation of all the forces acting on an object. In multi-body problems, drawing free-body diagrams for each component helps in visualizing how forces such as applied forces and contact forces act and interact, which is crucial for setting up the correct equations of motion.

Internal vs. External Forces

In the context of multiple interacting bodies, external forces are those applied from outside the system, while internal forces are the forces exerted between the bodies within the system. Although internal forces affect individual objects, they cancel out when considering the system as a whole, leaving only the external forces to determine the acceleration of the system.

Contact Forces

Contact forces are the interaction forces that are exerted between objects in physical contact. In problems involving blocks or other bodies pressing against each other, these forces (such as the pushing forces described) are key to understanding how the applied external force is distributed between the objects, ultimately affecting their individual and collective motion.

System Analysis

System analysis involves treating a collection of interacting objects as a single system to simplify the problem by considering its total mass and net external forces. This approach is particularly useful in dynamics problems with multiple bodies because it eliminates the need to account for internal contact forces, allowing for the direct application of Newton's Second Law to the entire system.

Newton's Second Law

Newton's Second Law is the principle that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This concept is fundamental when analyzing the motion of systems of objects, as it allows for the determination of acceleration when the net external force and total mass are known.

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