module 3 lecture 6: Newton's Laws of Motion, Forces, and Gravity

Newton's Laws of Motion

Overview of Newton's Laws

Newton's laws of motion form the foundation of classical mechanics, describing the relationship between the motion of an object and the forces acting upon it.

• First Law (Law of Inertia): Every object continues in a state of rest or uniform speed in a straight line unless acted on by a nonzero net force.

• Second Law: The acceleration of an object is directly proportional to the net force acting on it, is in the same direction as the net force, and is inversely proportional to its mass.

• Third Law: For every action, there is always an equal and opposite reaction.

Key Equations:

• Newton's Second Law: $F = ma$

• Weight: $W = mg$

Definitions:

• Mass: A measure of the amount of matter in an object, measured in kilograms (kg).

• Weight: The force of gravity acting on an object, measured in Newtons (N).

• Force: A push or pull on an object resulting from its interaction with another object.

• Acceleration: The rate of change of velocity of an object.

Inertia and Net Force

Inertia is the tendency of an object to resist changes in its state of motion. When the net force on an object is zero, its acceleration is zero, meaning its velocity remains constant. This is a direct consequence of Newton's First Law.

• If net force is zero: $a = 0$

• Implication: The object remains at rest or moves at constant velocity in a straight line.

Forces and Friction

Frictional Forces

Friction is a force that opposes the relative motion or tendency of such motion of two surfaces in contact. It arises due to the microscopic irregularities between surfaces.

• Friction reduces net force and thus affects acceleration.

• Friction occurs in solids, liquids, and gases (in fluids, it is often called drag or air resistance).

Falling Objects and Air Resistance

When objects fall through air, they experience a resistive force called air resistance or drag, which increases with velocity.

• Net force on a falling object: $F_{net} = mg - R$

• Acceleration: $a = \frac{mg - R}{m}$

• Air resistance (R): Often modeled as $R = bv$, where $b$ is a constant and $v$ is velocity.

Example: A feather in a vacuum falls at the same rate as a coin because there is no air resistance.

Terminal Velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.

• As an object falls, air resistance increases until it equals the weight of the object.

• At this point, net force is zero and acceleration ceases; the object continues at constant velocity (terminal velocity).

Example: A skydiver accelerates until air resistance equals their weight, then falls at terminal velocity.

Comparison Table: Heavy vs. Light Person with Parachutes

Person	Terminal Velocity	Who Reaches Ground First?
Heavy	Higher	Heavy person
Light	Lower	Slower

Additional info: The heavier person with the same-size parachute will reach the ground first because their terminal velocity is higher.

Newton's Third Law and Action-Reaction Pairs

Forces and Interactions

Forces always occur in pairs, known as action-reaction pairs. When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

• Action: Object A exerts a force on Object B.

• Reaction: Object B exerts an equal and opposite force on Object A.

• Action and reaction forces act on different objects.

Example: When you push on a wall, the wall pushes back on you with an equal and opposite force.

Identifying Action-Reaction Pairs

• Identify the interaction: What two objects are involved?

• State the action: Object A exerts a force on Object B.

• State the reaction: Object B exerts an equal and opposite force on Object A.

Example: Rocket propulsion: The rocket exerts a force on the exhaust gases (action), and the gases exert an equal and opposite force on the rocket (reaction).

Universal Law of Gravitation

Newton's Law of Universal Gravitation

Every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

• Equation: $F_g = G \frac{m_1 m_2}{r^2}$

• G: Universal gravitational constant ($6.674 \times 10^{-11} \; \mathrm{N\,m^2/kg^2}$)

Example: The gravitational attraction between Earth and an apple causes the apple to fall to the ground.

Summary Table: Newton's Three Laws

Law	Description	Key Equation
First	Object remains at rest or in uniform motion unless acted on by a net force	N/A
Second	Acceleration is proportional to net force and inversely proportional to mass	$F = ma$
Third	For every action, there is an equal and opposite reaction	N/A

Practice Questions (from notes)

• When a skydiver falls faster and faster, what happens to air resistance? It increases.

• When a skydiver continues to fall faster and faster, what happens to net force? It decreases.

• When a skydiver continues to fall faster and faster, what happens to acceleration? It decreases.

• When a cannon is fired, why are the accelerations of the cannon and cannonball different? Because their masses are different.

Key Takeaways

• Mass and weight are distinct: mass is measured in kilograms, weight in Newtons.

• Forces always come in pairs and act on different objects.

• Terminal velocity is reached when the force of air resistance equals the weight of the falling object.

• Newton's laws explain a wide range of physical phenomena, from falling objects to rocket launches.