Chapter 5: Applying Newton's Laws

Learning Outcomes

This chapter focuses on the application of Newton's laws of motion to various physical scenarios. Students will learn to:

• Use Newton's First Law to solve equilibrium problems.

• Apply Newton's Second Law to analyze accelerating objects.

• Understand and solve problems involving frictional forces.

• Analyze forces acting on objects in circular motion.

• Recognize the properties of the four fundamental forces of nature.

Introduction

Newton's three laws of motion provide the foundation for classical mechanics. While the laws themselves are simple, their application to real-world problems requires careful analysis and problem-solving skills. This chapter begins with equilibrium problems, where forces balance, and progresses to dynamic situations involving acceleration and more complex force interactions.

Newton's First Law and Equilibrium

Definition of Equilibrium

An object is in equilibrium when it is at rest or moving with constant velocity in an inertial frame of reference. In such cases, the net force acting on the object is zero.

• Newton's First Law: An object at rest remains at rest, and an object in motion remains in motion with constant velocity unless acted upon by a net external force.

• Mathematical Formulation:

Sum of forces in equilibrium: Component form:

Problem-Solving Strategy for Equilibrium Situations

Set Up

1. Draw a sketch of the physical situation.

2. Draw a free-body diagram for each object in equilibrium.

3. Identify all interactions (contact or otherwise) and calculate weight if mass is given ().

4. Include only forces acting on the object.

5. Choose and indicate coordinate axes in your diagram.

Execute

1. Resolve each force into components along the chosen axes.

2. Set the sum of all x-components and y-components of force to zero:

3. If multiple objects interact, repeat for each and use Newton's Third Law to relate forces.

4. Ensure you have as many independent equations as unknowns, then solve for the target variables.

Newton's Second Law and Dynamics

Definition and Application

When the net force on an object is not zero, the object accelerates. Newton's Second Law relates the net force to the acceleration:

• Each component of the net force equals the mass times the corresponding component of acceleration:

Problem-Solving Strategy for Dynamics Situations

Set Up

1. Sketch the situation and draw free-body diagrams for each moving object.

2. Label all forces, including weight ().

3. Choose coordinate axes and indicate them in the diagram.

4. Identify any additional equations needed (e.g., constraints from ropes or pulleys).

Execute

1. Resolve forces into components along the axes.

2. List knowns and unknowns, identifying target variables.

3. Write Newton's Second Law for each component and object:

4. Solve the equations for the target variables.

Free-Body Diagrams

Key Points

• Only forces acting on the object should be included in a free-body diagram.

• Acceleration vectors may be shown for reference but are not forces.

• Do not include as a force in the diagram.

Apparent Weight and Weightlessness

Definition

Apparent weight is the normal force exerted by a surface, which may differ from the actual weight due to acceleration.

• For a person of mass in an elevator accelerating with :

• If (free fall), and the person feels weightless.

Frictional Forces

Nature of Friction

Friction is a force that opposes relative motion between two surfaces in contact. It arises from molecular interactions at the surfaces.

Kinetic and Static Friction

• Kinetic friction () acts when an object slides over a surface:

• Static friction () acts when there is no relative motion:

• Static friction adjusts up to its maximum value; once exceeded, kinetic friction takes over.

Stick-Slip Phenomenon

Stick-slip occurs when static friction is overcome and kinetic friction begins, as seen in squeaky windshield wipers on dry glass.

Approximate Coefficients of Friction

Coefficients of friction vary by material. Typical values are:

Fluid Resistance and Terminal Speed

Definition

Fluid resistance (drag) opposes the motion of objects through fluids (liquids or gases) and depends on speed.

• A falling object reaches terminal speed when the drag force equals its weight:

• At terminal speed, acceleration is zero and velocity is constant.

Dynamics of Circular Motion

Uniform Circular Motion

For an object moving in a circle at constant speed, the net force and acceleration are directed toward the center (centripetal).

• Centripetal force:

• If the centripetal force is removed (e.g., string breaks), the object moves in a straight line (Newton's First Law).

• Centrifugal force is not a real force in inertial frames; it is a fictitious force observed in rotating frames.

Banked Curves

Banking a curve allows a car to turn without relying on friction. The required banking angle can be found by analyzing forces:

The Fundamental Forces of Nature

Overview

All forces in nature are manifestations of four fundamental interactions:

• Gravitational – attraction between masses

• Electromagnetic – interaction between charged particles

• Strong nuclear – binds protons and neutrons in the nucleus

• Weak nuclear – responsible for certain types of radioactive decay

Physicists aim to unify these forces into a single comprehensive theory.

Summary Table: Fundamental Forces

Example: The gravitational force keeps planets in orbit, while the electromagnetic force governs interactions between charged particles.

Additional info: Some context and table entries inferred from standard physics knowledge.