Newton's Laws of Motion

Chapter 5: Newton's Laws of Motion

Force and Mass

• Force:

  • Generally understood as a push or pull.

  • It is a vector quantity, meaning it has both magnitude and direction.

  • Forces can be categorized into two types:

  • Contact Forces:

    • Result from physical contact between two objects.

  • Examples include friction, tension, and normal forces.

  • Contact forces are significant in interactions where surfaces are touching.

  • Field Forces:

    • Act between two objects even when they are not in physical contact.

    • Also known as “action at a distance”.

    • Examples include gravitational force, electrical force, and magnetic force.

  • Mass:

  • Defined as the quantity of matter in an object.

  • It represents the resistance to change in motion or to force.

  • Mass is a scalar quantity and does not change with location (e.g., on Earth vs. in space).

Fundamental Forces

• The interactions at the atomic level involve fundamental forces which include:

  • Strong Nuclear Force:

  • The force that holds protons and neutrons together in the atomic nucleus.

  • Electromagnetism:

  • The force between charged particles.

  • Weak Nuclear Force:

  • Responsible for processes such as beta decay in particles.

  • Gravity:

  • The force of attraction between masses.

Newton’s First Law

• States that an object remains at rest or moves at a constant velocity unless acted upon by a nonzero net force.

• Net Force:

  • Defined as the vector sum of all external forces acting on the object.

• Consequence of this Law:

  • It presents the feasibility of space travel, as objects in the vacuum of space experience negligible forces leading them to maintain their state of motion.

Demonstration of Newton's 1st Law

• A physical example demonstrating the first law could involve a small object on a smooth surface remaining undisturbed until a force is applied.

Newton’s Second Law

• Formulated as:

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

  • Mathematically expressed as:
    \overrightarrow{a}\alpha\frac{\Sigma\overrightarrow{F}}{m} or \Sigma\overrightarrow{F}=m\overrightarrow{a}

  • Both force and acceleration are vector quantities, and the law is applicable in three-dimensional coordinates.

• Relationship of Force, Mass, and Acceleration:

  • If the mass is constant and the net force increases, acceleration also increases.

Units of Force

• The SI unit of force is the Newton (N), where:

  • 1 Newton is defined as the force required to accelerate a mass of 1 kg at a rate of 1 m/s².

  • 1N=1\frac{\operatorname{kg}\cdot m}{s^2}

• The US Customary unit of force is the pound (lb), where:

  • 1 N = 0.225 lb

Free Fall Revisited

• Key observations about free fall:

  • The greater the mass of an object, the greater its gravitational force of attraction toward the Earth.

  • Although heavier objects experience greater gravitational forces, they also possess greater inertia, which means they do not accelerate faster than lighter objects.

  • The acceleration due to gravity (g) is the same for all objects in free fall, approximately 10 m/s² (more accurately, 9.8 m/s²).

Weight

• Definition of weight:

  • The gravitational force acting on an object of mass m near the Earth’s surface is termed the weight (W) of the object.

  • Mathematically, weight can be expressed as:
    W=m\cdot g

  • Here, g represents the acceleration due to gravity, which is approximately 9.8 m/s² or 10 m/s² m/s}^2 for simpler calculations.

  • This formula serves as a specific case of Newton’s Second Law and ties into the Law of Universal Gravitation.

Newton’s Third Law

• It states that if two objects, say object 1 and object 2, interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1.

• This is summarized by the equation: \overrightarrow{F_{12}}_{}=-\overrightarrow{F_{21}}_{}

  • This assertion implies that isolated forces cannot exist; every action has an equal and opposite reaction.

Newton's Third Law Examples

• Demo of Action-Reaction:

  • Example 1: A tire pushes on the road when a car is moving (Action), and the road pushes back on the tire (Reaction) - “WHAP!”

  • Example 2: A rocket expelling gas downwards (Action), with the gas pushing the rocket upwards (Reaction) - “PIFF!”

  • Example 3: When a man pulls on a spring (Action), the spring exerts a pull back on the man (Reaction).

Newton’s Second Laws: Net Force & Component Form

• An object at rest or moving with constant velocity is said to be in equilibrium where the net force acting on the object is zero (as acceleration is also zero).

• To analyze forces in various dimensions, the second law’s equation can be broken into components:

  • In two dimensions, the equations are written as:
    \Sigma\overrightarrow{F_{x}}=m\cdot a_{x}

    \Sigma\overrightarrow{F_{y}}=m\cdot a_{y}

• This indicates that the sum of forces in each axis direction must equal zero when in equilibrium.

The Normal Force

• The normal force (\overrightarrow{n} ) represents the support force exerted perpendicular to a surface by an object resting on it.

• It is the reaction to the weight of the object (e.g., a TV on a table).

• The normal force is always directed perpendicularly to the surface of contact.

• \overrightarrow{n}=-\overrightarrow{n}^{\prime}$$

Tension

• When a cord is attached to a body and pulled taut, the force exerted by the cord on the body is referred to as tension (T), directed away from the body along the cord.

Free Body Diagram

• To properly analyze forces acting on an object, one must draw a free body diagram:

  • Identify all forces acting on the object of interest.

  • Neglect the masses of strings or ropes attached to the object, as they are often considered negligible.

  • Choose an appropriate coordinate system to analyze the forces effectively.

  • Note that an incorrect free body diagram typically leads to erroneous solutions in physics problems.