Forces and Newton's Laws: Study Notes for Physics for Life Sciences I (Lecture 7, Sections 4.4-4.8)

Forces and Newton's Laws

Newton's First Law

Newton's First Law, also known as the law of inertia, describes the behavior of objects when no net force acts upon them. It establishes the foundational concept that motion does not change unless acted upon by a force.

• Statement: An object at rest remains at rest, and an object in motion continues in a straight line at constant speed, unless acted upon by a net external force.

• Mathematical Form: $\vec{F} = 0$ $\vec{a} = 0$

• Implication: Objects experiencing no net force will not accelerate.

• Example: A hockey puck sliding on frictionless ice will keep moving in a straight line at constant speed.

What is a Force?

A force is a fundamental concept in physics, representing an interaction that can change an object's motion. Forces are vectors, meaning they have both magnitude and direction.

• Definition: A force is a push or pull on an object.

• Properties:

  • Has magnitude and direction (vector quantity).

  • Requires an agent (source of the force).

  • Can be a contact force (requires physical contact) or a long-range force (acts at a distance, e.g., gravity).

• Net Force: The vector sum of all forces acting on an object. $\vec{F}_{\text{net}} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \ldots$

• Example: Multiple people pushing a box in different directions; the box moves according to the net force.

Types of Forces

Forces can be classified based on their origin and nature. The following table summarizes common forces and their notations:

Force	Notation
General force	$\vec{F}$
Weight	$w$
Spring force	$\vec{F}_{sp}$
Tension	$\vec{T}$
Normal force	$\vec{n}$
Static friction	$f_s$
Kinetic friction	$f_k$
Drag	$\vec{D}$
Thrust	$\vec{F}_{thrust}$

Experimental Basis for Newton's Second Law

Experiments show that the motion of objects under constant force follows predictable patterns. These findings lead to Newton's Second Law.

• Key Observations:

  • An object pulled with a constant force moves with constant acceleration.

  • Acceleration is directly proportional to the applied force.

  • Acceleration is inversely proportional to the object's mass.

• Graphical Representation:

  • Acceleration vs. Force: Linear relationship.

  • Acceleration vs. Mass: Inverse relationship.

Newton's Second Law

Newton's Second Law quantifies the relationship between force, mass, and acceleration. It is a cornerstone of classical mechanics.

• Statement: The acceleration $a$ of an object is directly proportional to the net force $F$ acting on it and inversely proportional to its mass $m$.

• Mathematical Form: $a = \frac{F}{m}$ $\vec{a} = \frac{\vec{F}}{m}$

• Vector Form: $\vec{a} = \frac{\vec{F}_{\text{net}}}{m}$ $\vec{F}_{\text{net}} = m\vec{a}$

• Direction: The acceleration vector points in the same direction as the net force vector.

• Example: If a 2 kg object is acted on by a net force of 10 N, its acceleration is $a = \frac{10}{2} = 5$ m/s2.

Units of Force

Force is measured in newtons (N) in the SI system.

• Definition: One newton is the force required to accelerate a 1 kg mass by 1 m/s2.

• Unit Conversion: $1\,\text{N} = 1\,\text{kg} \cdot 1\,\text{m/s}^2$ $1\,\text{lb} \approx 4.45\,\text{N}$

Free-Body Diagrams

Free-body diagrams are essential tools for analyzing forces acting on an object. They help visualize and solve dynamics problems.

• Steps to Draw a Free-Body Diagram:

  1. Identify all forces acting on the object.

  2. Draw a coordinate system (axes may be tilted for inclined planes).

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

  4. Draw and label vectors for each force.

  5. Draw and label the net force vector beside the diagram.

• Example: A skier being pulled up a hill at constant speed has forces: tension (parallel to slope), friction (opposing motion), normal force (perpendicular to surface), and weight (vertically downward). If speed is constant, net force is zero.

Newton's Third Law

Newton's Third Law explains interactions between objects, stating that forces always occur in pairs.

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

• Action/Reaction Pair:

  • Each force in the pair acts on a different object.

  • Forces are equal in magnitude and opposite in direction.

• Mathematical Form: $\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$

• Examples:

  • Hammer and nail: Hammer exerts force on nail; nail exerts equal and opposite force on hammer.

  • Walking: Foot pushes backward on ground; ground pushes forward on foot.

  • Rocket propulsion: Rocket pushes gases backward; gases push rocket forward.

Summary Table: Newton's Laws

Law	Statement	Equation
First Law	Object remains at rest or in uniform motion unless acted upon by net force.	$\vec{F}_{\text{net}} = 0 \Rightarrow \vec{a} = 0$
Second Law	Net force causes acceleration proportional to force, inversely to mass.	$\vec{F}_{\text{net}} = m\vec{a}$
Third Law	For every action, there is an equal and opposite reaction.	$\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$

Applications and Examples

• Example: Racing Down the Runway A jet of mass 51,000 kg accelerates down a 940 m runway to takeoff speed. Using kinematics and Newton's Second Law:

  • Find acceleration using $v_f^2 = v_i^2 + 2a\Delta x$.

  • Calculate thrust: $F = ma$.

  • Thrust per engine: Divide total thrust by number of engines.

• Example: Wind-blown Basketball A basketball released in a breeze experiences weight downward and drag force to the right. The net force, and thus acceleration, points downward and to the right.

Key Concepts for Exam Preparation

• Understand and apply Newton's three laws to various physical situations.

• Be able to draw and interpret free-body diagrams.

• Classify and identify different types of forces.

• Use correct units and convert between them.

• Apply laws to solve problems involving forces, acceleration, and motion.

Additional info: Some context and examples have been expanded for clarity and completeness.