Chapter 4: Dynamics - Newton's Laws of Motion

Chapter 4: Dynamics: Newton's Laws of Motion

Chapter Overview

  • Purpose: Establish the connection between force and motion.

  • Key Topics:

    • Force

    • Newton’s First Law of Motion

    • Mass

    • Newton’s Second Law of Motion

    • Newton’s Third Law of Motion

    • Weight: The Force of Gravity and the Normal Force

    • Solving Problems with Newton’s Laws: Free-Body Diagrams

    • Problems Involving Friction and Inclines

Key Concepts

4-1 Force

  • Definition: A force is a push or a pull. It can cause an object at rest to move or change the velocity of a moving object.

  • Measurement: The magnitude of a force can be measured using a spring scale.

4-2a Newton’s First Law of Motion

  • Definition: Often called the law of inertia, it states that every object continues in its state of rest, or uniform velocity in a straight line, as long as no net force acts on it.

  • Inertial Reference Frames: An inertial reference frame is one in which Newton’s first law is valid, excluding rotating and accelerating frames.

What Causes Motion?

  • Experiential Insight: It appears necessary to continuously apply force to maintain motion (e.g., sliding a book across a table). However, objects slow down at varying rates based on friction.

  • In a frictionless environment, objects will continue in motion indefinitely, exemplified by the Voyager space probe.

4-2b What is a Force?

  • Characteristics of Forces:

    • A force acts on an object and has an agent (the object that applies the force).

    • A force is a vector quantity, represented by the symbol F with a magnitude F (strength of the force).

  • Types of Forces:

    • Contact Forces: Forces that act on objects through direct contact.

    • Long-Range Forces: Forces that act at a distance without physical contact.

4-2c Drawing Force Vectors

  1. Represent the object as a particle.

  2. Place the tail of the force vector on the particle.

  3. Draw the force vector as an arrow indicating the direction and length proportional to the force's size.

  4. Label the vector appropriately.

Combining Forces

  • When multiple forces (e.g., F₁, F₂, F₃) are exerted on an object, they combine to form a net force, defined as:
    ext{F}{net} = ext{F}1 + ext{F}2 + ext{F}3 + …

  • The net force is the resultant force; it replaces the original forces in calculation contexts.

4-3a Mass

  • Definition: Mass measures the inertia of an object, with SI units in kilograms (kg).

  • Distinction: Mass is intrinsic to an object, while weight is the force exerted on that object due to gravity.

  • Example: When moving from Earth to the moon (where gravitational acceleration is about 1/6 of Earth), weight decreases but mass remains constant.

4-6 Weight: The Force of Gravity and the Normal Force

  • Weight Definition: The gravitational pull of the Earth on an object, and is directed vertically downward.

  • Normal Force: The force exerted by a surface perpendicular to the contact surface, balancing the weight when an object is at rest on the surface.

4-5 Newton’s Third Law of Motion

  • Definition: Whenever one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first.

  • Application of the Law: Forces in this law act on different objects and should not be confused as acting on the same object.

Problem-Solving Strategies

Free-Body Diagrams

  • Free-body diagrams are crucial in dynamic problem-solving. They represent the object of interest as a particle and display all acting forces.

  • Steps to draw one:

    1. Identify all forces acting on the object.

    2. Establish a coordinate system aligned with the situation (e.g., tilted for inclined planes).

    3. Represent the object as a dot at the origin of the axes.

    4. Draw labeled vectors for each force identified.

    5. Annotate the net force vector alongside the diagram, ensuring it points in the same direction as the acceleration vector.

4-7 Solving Problems with Newton’s Laws Using Free-Body Diagrams

  1. Sketch the scenario.

  2. Draw a free-body diagram.

  3. Resolve vectors into components.

  4. Apply Newton’s second law (For example): ext{F}_{net} = ma

  5. Solve the equations.

Summary of Key Laws

Newton’s First Law:

  • An object at rest will stay at rest; an object in motion continues in motion at constant velocity unless a net force acts on it.

Newton’s Second Law:

  • The relationship expressed as a = rac{F_{net}}{m} implies that acceleration is proportional to net force and inversely proportional to mass.

Newton’s Third Law:

  • For every action, there is an equal and opposite reaction.

Weight

  • Weight can be expressed in SI units as ext{W} = mg, where g is the acceleration due to gravity.

Friction Forces

  • Kinetic friction can be modeled as F{fr} = ext{µ}k FN, while static friction can be expressed F{fr} ext{≤} ext{µ}s FN, resulting in distinguishing between the two depending on whether objects are moving or at rest.