Problem 17–78 | Speed of Connected Cylinders with Pulley Rotation | Chapter 17 Dynamics

Problem 17–78 | Speed of Connected Cylinders with Pulley Rotation | Chapter 17 Dynamics
Two cylinders A and B, having weights of 10 lb and 5 lb respectively, are attached to the ends of a cord which passes over a 3-lb pulley (disk). If the cylinders are released from rest, determine their speed at t=0.5 s. The cord does not slip on the pulley. Neglect the mass of the cord.

In this problem, we analyze the motion of a connected system involving translating masses and a rotating pulley using the principles of rigid body kinetics, no-slip constraint, and Newton–Euler equations of motion.

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

Converting weights of cylinders and pulley into mass values
Identifying the acceleration directions of cylinders A and B
Drawing free-body diagrams for both hanging masses
Drawing the free-body diagram of the rotating pulley
Applying Newton’s second law to each cylinder
∑F=ma
Applying rotational equation of motion to the pulley
∑M
O
​

=I
O
​

α
Using the no-slip condition between cord and pulley
a=rα
Relating linear accelerations of both cylinders
Solving the coupled system of equations for acceleration
Using kinematics to determine velocity at t=0.5 s
v=at (constant acceleration)
Interpreting how pulley inertia affects system acceleration

This problem is essential for understanding coupled translation–rotation systems and how pulley inertia influences the motion of connected bodies.

This video is especially useful for:

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

Keywords:
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