A force is fundamentally a push or a pull. It is an interaction that, when unopposed, causes a change in an object's state of motion. A force is a vector quantity, meaning it has both magnitude (how strong it is) and direction.

● Effects of Force:
○ Causes a stationary object to start moving.
○ Causes a moving object to stop.
○ Changes an object's speed (speeds up or slows down).
○ Changes an object's direction of motion.
○ Can also cause a change in an object's shape (deformation), even without changing its motion.

● Unit of Force: The standard international (SI) unit for force is the Newton (N), named after Sir Isaac Newton. One Newton is roughly the force needed to accelerate a 1 kg mass at 1 m/s².

Forces can be broadly classified based on whether they require direct physical contact between objects.

2.2.1 Contact Forces:
These forces arise when objects are in direct physical contact.
1. Normal Force (FN or N): This is the force exerted by a surface perpendicular to the surface of contact with an object. It acts to prevent objects from penetrating the surface they are resting on or against.
○ Example: A book resting on a table experiences an upward normal force from the table, balancing its weight.
2. Friction Force (Ff): This force opposes the relative motion or attempted motion between two surfaces in contact. It always acts parallel to the surfaces.
○ Static Friction: Acts when surfaces are at rest relative to each other, preventing motion from starting.
○ Kinetic (or Sliding) Friction: Acts when surfaces are sliding past each other, opposing the ongoing motion.
○ Factors affecting friction: Type of surfaces in contact (roughness), normal force pressing the surfaces together.
○ Examples: The force that allows you to walk without slipping, the force that slows down a rolling ball.
3. Tension Force (FT or T): This is the pulling force transmitted axially through a string, rope, cable, chain, or similar flexible connector when it is pulled taut by forces acting from opposite ends. Tension always acts along the direction of the string/rope.
○ Example: When you pull a wagon with a rope, the force you apply is transmitted as tension along the rope to the wagon.
4. Applied Force (Fapp): A general term for any external force applied to an object by a person or another object.

Sir Isaac Newton, in his Philosophiae Naturalis Principia Mathematica (1687), laid down the foundational principles that govern motion.

2.3.1 Newton's First Law of Motion (Law of Inertia)
"An object at rest remains at rest, and an object in motion remains in motion with constant velocity (constant speed in a straight line) unless acted upon by a non-zero net force."
● Inertia: This law introduces the concept of inertia, which is the inherent property of an object to resist changes in its state of motion. The more mass an object has, the greater its inertia.
● State of Motion: "At rest" is a state of motion. "Constant velocity" (constant speed and constant direction) is also a state of motion.
● Unbalanced/Net Force: For an object's motion to change (to accelerate), there must be a net (or resultant) force acting on it. If the net force is zero, the object's velocity will not change.
● Everyday Examples:
○ When a bus suddenly brakes, passengers lurch forward due to their inertia.
○ A book on a table stays put until you push or pull it.
○ A hockey puck slides for a long time on ice because of very low friction (minimal unbalanced force).

These terms are often confused in common language, but their physical meanings are distinct.
● Mass (m):
○ Definition: A fundamental measure of the amount of matter an object contains. It is also a measure of an object's inertia – its resistance to changes in motion.
○ Quantity Type: Scalar quantity (magnitude only).
○ Units: Kilograms (kg), grams (g).
○ Constancy: Mass is an intrinsic property of an object and remains constant regardless of its location in the universe (e.g., your mass on Earth is the same as your mass on the Moon or in space).
● Weight (W or Fg):
○ Definition: The force of gravity acting on an object's mass. It is a force exerted by a gravitational field.
○ Quantity Type: Vector quantity (magnitude and direction, always downwards towards the center of the gravitational source).
○ Units: Newtons (N), since it is a force.
○ Variability: Weight depends on the strength of the gravitational field the object is in.
■ Equation: W=mg
■ g is the acceleration due to gravity. On Earth's surface, g≈9.8 m/s² (often approximated as 10 m/s² for simplicity in many problems). On the Moon, g is much smaller, so an object's weight there would be less than on Earth, even though its mass remains the same.
Example: An astronaut with a mass of 70 kg.
● On Earth (g≈9.8 m/s²): Weight = 70 kg×9.8 m/s²=686 N.
● On the Moon (g≈1.6 m/s²): Weight = 70 kg×1.6 m/s²=112 N. The astronaut's mass (70 kg) remains constant in both locations.

When multiple forces act on an object, their combined effect determines the object's motion.
● Resultant Force (Net Force, ΣF or Fnet): This is the single force that represents the combined effect of all individual forces acting on an object. It is the vector sum of all forces.
○ Adding Forces:
■ If forces act in the same direction, simply add their magnitudes. (e.g., 5 N East + 3 N East = 8 N East)
■ If forces act in opposite directions, subtract their magnitudes, and the resultant force is in the direction of the larger force. (e.g., 5 N East + 3 N West = 2 N East)
■ For forces at right angles, the Pythagorean theorem and trigonometry can be used (though usually introduced later or for simpler cases at this level).
○ Effect of Net Force: According to Newton's Second Law, the net force causes an object to accelerate. If Fnet = 0, the object's velocity will change.
● Equilibrium: An object is said to be in equilibrium when the resultant force acting on it is zero (Fnet = 0).
○ Consequence: According to Newton's First Law, if the net force is zero, the object's acceleration is also zero (a=0).
○ Two States of Equilibrium:
■ Static Equilibrium: The object is at rest and remains at rest. (e.g., a book on a table, a car parked).
■ Dynamic Equilibrium: The object is moving at a constant velocity (constant speed in a straight line) and continues to do so. (e.g., a car cruising at a steady speed on a straight road, a skydiving parachutist falling at terminal velocity).
Example: A tug-of-war where both teams pull with equal and opposite forces. The rope is in equilibrium, so it does not accelerate, even though large forces are being applied.

Pressure is a concept that describes how a force is distributed over a surface. It's not just about the magnitude of the force, but also the area over which it acts.
● Definition: Pressure is defined as the force applied perpendicularly to a surface, divided by the area over which that force is distributed.
Pressure (P) = Area (A) / Force (F)
● Units:
○ The SI unit for pressure is the Pascal (Pa), which is equivalent to one Newton per square meter (1 Pa = 1 N/m²).
○ Other common units include kilopascals (kPa), atmospheres (atm), pounds per square inch (psi), and bar.
● Implications:
○ For a given force, a smaller area results in higher pressure.
○ For a given force, a larger area results in lower pressure.
● Applications of Pressure in Everyday Life and Technology:
○ Cutting Tools (Knives, Axes): These are designed with very sharp edges, which means they have a very small contact area. When a force is applied to the handle, it results in extremely high pressure at the blade's edge, allowing it to cut through materials.
○ Walking on Snow/Soft Ground:
■ High Heels/Boots: Your weight is concentrated on a small area, creating high pressure that causes you to sink into soft ground.
■ Snowshoes/Skis: These have a large surface area. By distributing your weight over this large area, they significantly reduce the pressure on the snow, allowing you to walk on top of it without sinking.
○ Foundations of Buildings: Large buildings have wide foundations to spread their immense weight over a large area of ground. This reduces the pressure exerted on the soil, preventing the building from sinking or cracking the ground.
○ Tires: Car tires are wide and inflated to a specific pressure to distribute the weight of the vehicle over a sufficient area, providing good grip and preventing them from sinking into soft surfaces.
○ Hydraulic Systems (Pascals' Principle): This principle states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This is the basis for:
■ Hydraulic Brakes: A small force applied to a small piston in the brake pedal creates a certain pressure. This pressure is transmitted through the brake fluid to larger pistons at the wheels, generating a much larger force to stop the car.
■ Hydraulic Lifts (Jacks): A small force applied over a small area can lift a very heavy object by generating a large force over a larger area.
Example Problem: A brick has a mass of 2 kg. Its base dimensions are 0.2 m by 0.1 m.
1. Calculate the force (weight) it exerts on the ground. (g=9.8 m/s²)
○ F=W=mg=2 kg × 9.8 m/s² = 19.6 N
2. Calculate the area of its base.
○ A=0.2 m × 0.1 m = 0.02 m²
3. Calculate the pressure it exerts.
○ P=F/A=19.6 N/0.02 m²=980 Pa