Chapter 4: Newton's Laws of Motion and Forces

Types of Forces

Forces are interactions that cause changes in the motion of objects. Understanding the different types of forces is fundamental in analyzing physical systems.

• Contact Forces: Forces that arise from physical contact between objects (e.g., friction, normal force, tension).

• Field Forces: Forces that act over a distance without direct contact (e.g., gravitational, electromagnetic).

• Examples: Friction opposes motion, gravity pulls objects toward Earth, tension acts along ropes or cables.

Vector Addition of Forces

Forces are vector quantities, meaning they have both magnitude and direction. The net force is found by vector addition.

• Resultant Force: The sum of all forces acting on an object.

• Vector Addition: Use graphical (parallelogram or triangle method) or analytical (component-wise) methods.

• Equation:

Newton’s Three Laws of Motion

Newton's laws describe the relationship between forces and motion.

• First Law (Law of Inertia): An object remains at rest or in uniform motion unless acted upon by a net external force.

• Second Law: The acceleration of an object is proportional to the net force and inversely proportional to its mass.

• Equation:

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

Mechanical Equilibrium

Mechanical equilibrium occurs when the net force on an object is zero.

• Static Equilibrium: Object at rest.

• Dynamic Equilibrium: Object moving at constant velocity.

• Condition:

Mass vs. Weight

Mass and weight are related but distinct physical quantities.

• Mass: Measure of the amount of matter in an object (scalar, SI unit: kg).

• Weight: Force due to gravity acting on mass (vector, SI unit: N).

• Equation:

• Example: A 2 kg object on Earth has a weight of N.

Chapter 6: Work and Kinetic Energy

Mathematical Definition of Work

Work is the energy transferred by a force acting over a distance.

• Equation (Constant Force):

• Equation (Variable Force):

Kinetic Energy

Kinetic energy is the energy of motion.

• Equation:

• Example: A 1 kg object moving at 3 m/s has J.

The Work-Energy Theorem

The work done by the net force on an object equals the change in its kinetic energy.

• Equation:

Calculating Work Done by a Varying Force

When force varies with position, work is calculated using integration.

• Equation:

Power

Power is the rate at which work is done or energy is transferred.

• Equation:

• Instantaneous Power:

• Example: If 100 J of work is done in 5 s, W.

Chapter 7: Potential Energy and Conservation of Energy

Gravitational Potential Energy

Potential energy due to an object's position in a gravitational field.

• Equation:

Elastic Potential Energy

Energy stored in a stretched or compressed spring.

• Equation:

• Example: A spring with N/m and m has J.

Conservation of Mechanical Energy

In the absence of nonconservative forces, the total mechanical energy (kinetic + potential) remains constant.

• Equation:

Conservative vs. Nonconservative Forces

Conservative forces (e.g., gravity, spring force) store energy as potential; nonconservative forces (e.g., friction) dissipate energy.

• Conservative: Work done is path-independent; energy can be fully recovered.

• Nonconservative: Work done is path-dependent; energy is lost as heat or other forms.

Internal Energy and Work Done by Nonconservative Forces

Nonconservative forces increase internal energy (e.g., thermal energy due to friction).

• Equation:

• Example: Friction converts mechanical energy to heat.

Conservation of Energy Including Internal Energy

The total energy (mechanical + internal) is conserved in a closed system.

• Equation:

Mathematical Relation Between Force and Potential Energy

The force associated with a potential energy function is the negative gradient of the potential.

• Equation:

Chapter 8: Momentum, Impulse, and Collisions

Momentum and Its Relation to Force and Impulse

Momentum is the product of mass and velocity; impulse is the change in momentum due to a force applied over time.

• Momentum Equation:

• Impulse Equation:

Conservation of Momentum

In a closed system, total momentum remains constant if no external forces act.

• Equation:

Elastic, Inelastic, and Completely Inelastic Collisions

Collisions are classified by how kinetic energy is conserved.

• Elastic: Both momentum and kinetic energy are conserved.

• Inelastic: Momentum is conserved, but kinetic energy is not.

• Completely Inelastic: Colliding objects stick together after collision.

Center of Mass and Its Relation to Momentum and Force

The center of mass is the weighted average position of all mass in a system. The motion of the center of mass reflects the net external force.

• Equation:

• Relation: The total momentum of a system equals the mass times the velocity of the center of mass.

• Equation:

• Example: In a collision, the center of mass moves according to the net external force.