Newton's Laws of Motion, Friction, Mass, Weight, and Terminal Velocity

Newton's Laws of Motion

Newton's First Law (Law of Inertia)

Newton's First Law states that an object at rest remains at rest, and an object in motion continues in motion with constant speed and direction unless acted upon by a net external force. This law is also known as the Law of Inertia.

• Inertia: The tendency of an object to resist changes in its state of motion.

• Key Point: No net force is required to keep an object moving at constant speed in a straight line.

• Example: An astronaut in space demonstrates that an object in motion stays in motion unless acted upon by an outside force.

Newton's Second Law

Newton's Second Law relates the net force acting on an object to its mass and acceleration. It provides a quantitative description of the changes that a force can produce on the motion of a body.

• Formula: $F = ma$

• Definitions:

  • F: Net force acting on the object (in Newtons, N)

  • m: Mass of the object (in kilograms, kg)

  • a: Acceleration of the object (in meters per second squared, m/s2)

• Key Points:

  • Acceleration is directly proportional to net force.

  • Acceleration is inversely proportional to mass.

  • If net force doubles, acceleration doubles (for constant mass).

  • If mass doubles, acceleration halves (for constant force).

• Example: If you apply the same force to two objects of different mass, the lighter object will accelerate more.

Newton's Third Law

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that forces always occur in pairs.

• Key Point: If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

• Example: When a rocket expels gas backward, the rocket moves forward due to the reaction force.

Friction

The Force of Friction

Friction is a force that opposes the motion of objects. It arises from the interactions between the surfaces in contact.

• Depends on:

  • The types of materials in contact

  • How much the surfaces are pressed together

• Origin: Due to microscopic surface bumps and the 'stickiness' of atoms on the surfaces.

• Types: Friction can occur with sliding objects, in water, or in air (air resistance).

• Example: Friction between a crate and a smooth wood floor is less than that on a rough floor.

Mass and Weight

Definitions

• Mass: The quantity of matter in an object; a measure of inertia. Unit: kilogram (kg).

• Weight: The force of gravity acting on an object. Unit: Newton (N) or pound (lb).

• Relationship: $W = mg$

• g: Acceleration due to gravity (on Earth, $g = 9.8\ \text{m/s}^2$; on Moon, $g = 1.62\ \text{m/s}^2$)

• Conversion: $1\ \text{kg} = 2.21\ \text{lb} = 10\ \text{N}$ (approximate at Earth's surface)

• Example: A 1 kg mass weighs 9.8 N on Earth.

Mass vs. Weight

• Mass is constant regardless of location.

• Weight changes with the strength of gravity.

• Example: An object has the same mass on Earth and the Moon, but its weight is less on the Moon.

Free Fall and Terminal Velocity

Free Fall (No Air Resistance)

When an object falls under the influence of gravity alone (no air resistance), it is said to be in free fall.

• Acceleration: All objects accelerate at the same rate regardless of mass ($g = 9.8\ \text{m/s}^2$ on Earth).

• Example: A 1-kg and a 10-kg iron ball dropped from rest will have the same acceleration.

• Velocity after t seconds: $v = gt$

Nonfree Fall (With Air Resistance)

When air resistance is significant, the motion of a falling object is affected by both gravity and drag force.

• Forces:

  • Gravity pulls downward.

  • Air resistance (drag) acts upward.

• Factors affecting air resistance:

  • Speed of the object

  • Frontal surface area

• Net Force: $F_{\text{net}} = mg - F_{\text{drag}}$

• Acceleration: $a = \frac{F_{\text{net}}}{m}$

Terminal Velocity

Terminal velocity is reached when the force of air resistance equals the weight of the object, resulting in zero net force and zero acceleration. The object then falls at a constant speed.

• Terminal speed: The speed at which acceleration terminates (net force is zero).

• Terminal velocity: Terminal speed with direction specified.

• Example: Skydivers reach terminal velocity when the upward drag force equals their weight.

Comparing Free Fall and Nonfree Fall

• In vacuum: All objects fall at the same rate (no air resistance).

• With air: Lighter objects (like feathers) reach terminal velocity quickly and fall slowly; heavier objects (like coins) fall faster and reach the ground sooner.

Summary Table: Mass vs. Weight

Property	Mass	Weight
Definition	Amount of matter in an object	Force of gravity on an object
Unit	kilogram (kg)	Newton (N)
Depends on location?	No	Yes
Formula	—	$W = mg$

Key Equations

• Newton's Second Law: $F = ma$

• Weight: $W = mg$

• Velocity in free fall: $v = gt$

• Net force with air resistance: $F_{\text{net}} = mg - F_{\text{drag}}$

• Acceleration with air resistance: $a = \frac{mg - F_{\text{drag}}}{m}$