Boxes A and B are connected to each end of a light vertical...

Boxes $A$ and $B$ are connected to each end of a light vertical rope (Fig. $\mathbf{P 4 . 4 5}$ ). A constant upward force $F=80.0 \mathrm{~N}$ is applied to box $A .$ Starting from rest, box $B$ descends $12.0 \mathrm{~m}$ in $4.00 \mathrm{~s}$. The tension in the rope connecting the two boxes is $36.0 \mathrm{~N}$. What are the masses of $(\mathrm{a})$ box $B,(\mathrm{~b})$ box $A ?$

Key Concepts

Newton's Second Law

Newton's Second Law, expressed as F_net = m * a, is the foundational concept for analyzing the forces and accelerations on objects. It allows the determination of an object's mass when the net force acting on it and its acceleration is known, or vice versa, and is essential in problems involving dynamics of connected objects.

Kinematics of Constant Acceleration

Kinematics of constant acceleration describes the motion of objects under uniformly accelerating conditions, using equations that relate displacement, initial velocity, time, and acceleration. This concept is used to determine the acceleration of an object given its displacement and time, which is crucial for linking the observed motion to the forces acting on the system.

Tension in Rope Systems

Tension represents the pulling force transmitted along a rope, string, or cable when forces are applied at its ends. In many mechanical problems involving connected masses, assuming a massless and inextensible rope simplifies the analysis, as the tension throughout the rope is constant. This concept is vital for setting up force balance equations for each object in the system.

Free-Body Diagram Analysis

Free-body diagrams are graphical representations that isolate an object and depict all the forces acting on it. They are an essential tool in mechanics, as they help in systematically applying Newton’s laws to individual components of a system, allowing for the accurate formulation of equations that describe the relationships between forces, masses, and accelerations.

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