Chapter 5: Applying Newton’s Laws

Overview

This chapter focuses on the application of Newton’s laws to solve problems involving equilibrium, dynamics, friction, drag, and interacting objects. It provides strategies for analyzing forces, constructing free-body diagrams, and understanding the physical principles governing motion and force interactions.

Equilibrium

Static and Dynamic Equilibrium

Equilibrium occurs when the net force acting on an object is zero. There are two types:

• Static Equilibrium: The object is at rest.

• Dynamic Equilibrium: The object moves in a straight line at constant speed.

In both cases, the sum of the forces in each direction must be zero:

Problem-Solving Strategy for Equilibrium

• Draw a sketch of the physical situation.

• Draw a free-body diagram for each object.

• Identify all forces acting on the object.

• Choose coordinate axes and resolve forces into components.

• Set the sum of all force components to zero and solve for unknowns.

Dynamics and Newton’s Second Law

Newton’s Second Law

Newton’s second law relates the net force on an object to its acceleration:

• Component form: ,

Problem-Solving Strategy for Dynamics

• Draw a sketch and free-body diagram for each moving object.

• Label all forces, including weight ().

• Choose coordinate axes and resolve forces.

• Write Newton’s second law for each component.

• Solve for acceleration, velocities, positions, or unknown forces.

Mass and Weight

Definitions

• Mass: A measure of an object’s inertia; it does not change with location.

• Weight: The gravitational force exerted on an object by a planet; .

Apparent Weight

Apparent weight is the contact force supporting an object, which can differ from true weight when accelerating:

• In an elevator accelerating upward:

• In free fall: (apparent weightlessness)

Normal Forces

Normal Force on Flat and Inclined Surfaces

The normal force is the perpendicular contact force exerted by a surface. On an incline, it is always perpendicular to the surface, not necessarily vertical.

Friction

Types of Friction

• Static Friction: Prevents relative motion;

• Kinetic Friction: Acts during sliding;

• Rolling Friction: Occurs with rolling objects; typically much less than kinetic friction.

Static and Kinetic Friction: Examples

• Static friction adjusts to oppose motion up to a maximum value.

• Kinetic friction remains constant once sliding begins.

Coefficients of Friction

The coefficient of friction depends on the materials in contact. Typical values are provided in tables.

Stick-Slip Phenomenon

Stick-slip occurs when static friction alternates with kinetic friction, as seen in squeaky windshield wipers.

Drag Forces

Fluid Resistance and Terminal Speed

Drag is a resistive force experienced by objects moving through fluids. Terminal speed is reached when drag equals weight:

• At terminal speed:

• Before terminal speed:

Reynolds Number and Drag Models

• High Reynolds Number: Drag force proportional to

• Low Reynolds Number: Drag force proportional to (Stokes' law)

Interacting Objects

Newton’s Third Law

Every force occurs as one member of an action/reaction pair. The two members act on different objects, are equal in magnitude, and opposite in direction.

Objects in Contact

• Draw separate free-body diagrams for each object.

• Identify action/reaction pairs.

• Objects in contact have the same acceleration.

Ropes and Pulleys

Tension in Ropes

For massless ropes, the tension is the same throughout and equals the force applied at the ends.

Pulleys

For massless, frictionless pulleys, the tension in the rope is unchanged as it passes over the pulley.

Summary of Key Concepts

• Equilibrium:

• Dynamics:

• Weight:

• Friction: ,

• Drag: (high Re), (low Re)

• Action/reaction pairs: Equal and opposite forces on interacting objects

• Tension: Same throughout a massless rope, unchanged by ideal pulleys