CHAPTER 3 -- FORCES AND CLASSICAL DYNAMICS
Dynamics is the study of forces and their effect on motion. While kinematics describes "how" things move, dynamics explains "why" they move.
3.1 NEWTON'S LAWS OF MOTION
Sir Isaac Newton formulated three fundamental laws that form the foundation of classical mechanics.
Newton's First Law (Law of Inertia):
A body remains at rest, or in motion at a constant velocity in a straight line, unless acted upon by a net external force.
This implies that force is not required to maintain motion, but rather to change it.
Newton's Second Law (Fundamental Law of Dynamics):
The rate of change of momentum of a body is directly proportional to the net force applied to it.
F_net = dp / dt
Since momentum p = m * v, for a system with constant mass, this simplifies to:
F_net = m * a
where F_net is the vector sum of all forces, m is mass, and a is acceleration.
This equation defines the unit of force, the Newton (N). 1 N = 1 kg * m/s^2.
Newton's Third Law (Action-Reaction):
For every action, there is an equal and opposite reaction.
If object A exerts a force F_AB on object B, then object B exerts a force F_BA on object A such that:
F_AB = - F_BA
These forces always act on different objects and therefore never cancel each other out in the context of a single object's free-body diagram.
3.2 FORCE FIELDS
Forces can be contact forces (e.g., friction, tension, normal force) or field forces (action-at-a-distance). A "field" permeates space and exerts a force on a particle situated within it.
Gravitational Field:
Any object with mass creates a gravitational field g around it. Another mass m placed in this field experiences a force F_g = m * g.
Near Earth's surface, g approx 9.8 m/s^2, pointing distinctively downward.
Electromagnetic Fields:
Electric charges create electric fields, and moving charges create magnetic fields. These fields mediate the electromagnetic interaction.
The concept of fields eliminates the problem of instantaneous action-at-a-distance, suggesting that changes in the source propagate through the field at a finite speed (the speed of light).
3.3 MASS VS WEIGHT
In everyday language, mass and weight are often used interchangeably, but in physics, they are distinct.
Mass (m):
- A scalar quantity representing the amount of matter in an object.
- It is a measure of inertia (resistance to acceleration).
- Mass is intrinsic; it does not change regardless of location (Earth, Moon, space).
Weight (W):
- A vector quantity representing the gravitational force acting on an object.
- W = m * g
- Weight depends on the local gravitational field strength. An astronaut weighs less on the Moon than on Earth, but their mass remains the same.
3.4 INERTIA
Inertia is the tendency of an object to resist changes in its state of motion. It is directly quantifying by mass.
- A massive truck has high inertia: it is hard to start moving and hard to stop.
- A ping-pong ball has low inertia: it is easy to accelerate or decelerate.
The equivalence of "inertial mass" (the m in F=ma) and "gravitational mass" (the m in F_g=mg) is a deep principle in physics (the Equivalence Principle) that led Einstein to the General Theory of Relativity.
3.5 ACTION-REACTION PAIRS
Identifying correct action-reaction pairs is crucial for solving mechanics problems.
Example: A book resting on a table.
Forces on the book:
1. Gravity (Earth pulling down): W
2. Normal force (Table pushing up): N
Since the book is at rest, N = W (in magnitude).
However, N and W are NOT an action-reaction pair because they act on the same object (the book).
The Action-Reaction pairs are:
- Pair 1: Earth pulls Book down (Gravity) <--> Book pulls Earth up (Gravity).
- Pair 2: Book pushes Table down (Contact) <--> Table pushes Book up (Normal Force).
