Lecture Notes: Constrained Motion and Pulleys

Introduction

• Today's session is an extension of Newton's laws, covering constrained motion.
• Multiple pulleys and their advantages will be discussed.
• Constrained motion applies to many machines.
• Instructor: Shreyas, Physics Master Teacher at Vedantu.

Schedule Overview

• Today: Constrained motion with movable pulleys.
• Friday: Non-inertial frames and pseudo forces.
• Saturday: Special session on EMI (Electromagnetic Induction).

Constrained Motion

Definition

• Constrained motion: Motion restricted in relation to the motion of other objects.
• Example: If Ankit moves 1 meter, Madhula moves 2 meters.

Types of Constraints

1. Pulleys and Strings: Pulleys that assist in lifting loads.
2. Inclined Planes: Use of wedges and rods.

Pulley System Dynamics

• Key Rule: Length of the string remains constant; if one part moves, others must adjust.
• If string pulled on one end, the whole system responds as the string length does not change.
• Velocity components along the string must be equal (v1*cos(θ) = v2 for different points on the same string).

Velocity Relationships

• When working with pulleys, the velocity of connected objects relates through the strings they share.
• Example: If one mass moves down by a certain distance, the other will move a proportional distance as dictated by the string arrangement.
• Acceleration relationships can likewise be derived from the velocity relationships.

Example Problem: Pulley Arrangements

• When masses connected over pulleys, use constraints to find relationships between velocities and accelerations.
• For fixed pulleys: if mass M moves down at velocity v1, related mass moves at different speed depending on the number of strings.

Assumptions and Considerations

• Strings are assumed to be inelastic (do not stretch) in ideal physics problems.
• Simplifying assumptions about the system (massless pulleys, ideal frictionless strings).

Examples and Practice Problems

1. Given two masses, determine their velocities based on pulley configurations and applied forces.
2. Use different approaches (derivative method, component method) to solve current constraints.
3. Compare outcomes and understand which is more efficient during examinations.

Special Cases: Wedges and Rods

• If a rod is placed on an inclined wedge, the same principles apply: find component velocities perpendicular to the surfaces in contact.
• Key principle: points on the surfaces in contact should maintain equal velocities perpendicular to their surfaces.

Final Thoughts

• Solve practice problems regularly to master these concepts.
• Make use of provided PDFs and materials after each class to reinforce learning.

Homework

• Two questions related to constrained motion to solve and discuss in the comments.