Problem 17–79 | Acceleration of Block A with Massive Pulley | Chapter 17 Dynamics

Problem 17–79 | Acceleration of Block A with Massive Pulley | Chapter 17 Dynamics
The two blocks A and B have masses of 5 kg and 10 kg, respectively. If the pulley can be treated as a disk of mass 3 kg and radius 0.15 m, determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley.

In this problem, we analyze the motion of a connected block–pulley system using the principles of rigid body kinetics, rotational dynamics, and Newton–Euler equations of motion.

The solution is presented in a clear, step-by-step manner and includes:

Identifying the masses of blocks A and B and the pulley
Determining the direction of motion of the system
Drawing free-body diagrams for both blocks
Drawing the free-body diagram of the pulley (treated as a disk)
Converting pulley mass into mass moment of inertia
I=
2
1
​

mr
2
Applying Newton’s second law to block A
∑F=ma
Applying Newton’s second law to block B
Applying rotational equation of motion to the pulley
∑M
O
​

=I
O
​

α
Using the no-slip constraint
a=rα
Forming a system of equations linking tensions, acceleration, and angular motion
Solving for the acceleration of block A
Interpreting the effect of pulley inertia on system acceleration

This problem is essential for understanding how pulley mass and rotational inertia influence the acceleration of connected bodies in dynamic systems.

This video is especially useful for:

Engineering Mechanics – Dynamics
Rigid Body Kinetics
Pulley Systems with Mass
Newton–Euler Equations
No-Slip Constraint Motion
Exam and Homework Preparation

Keywords:
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