Physics Formula Matriculation

Physics Formulas for Matriculation: Comprehensive Guide with Examples

Physics is a fundamental subject in the field of science that helps us understand the natural world through the study of matter, energy, and their interactions. For matriculation exams, mastering key physics formulas is crucial for problem-solving in various topics, including mechanics, electromagnetism, and optics. This guide provides essential physics formulas for matriculation with examples to help you understand their applications.

1. Mechanics Formulas

Newton's Laws of Motion

Newton's Laws of Motion form the foundation of mechanics and describe how forces affect the motion of objects.

First Law (Law of Inertia): An object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an external force.
Second Law (Force Formula): F = m × a (where F = force in Newtons, m = mass in kg, a = acceleration in m/s²).
Third Law (Action and Reaction): For every action, there is an equal and opposite reaction.

Example: Calculate the force exerted on a 10 kg object accelerating at 5 m/s².

Solution:

Using F = m × a,

F = 10 × 5 = 50 N

Kinematic Equations of Motion

These equations describe the motion of an object moving with constant acceleration.

Final velocity (v): v = u + at
Displacement (s): s = ut + 0.5at²
Velocity squared (v²): v² = u² + 2as

Where u is the initial velocity, v is the final velocity, a is acceleration, and t is time.

Example: A car starts from rest (u = 0) and accelerates at 3 m/s² for 4 seconds. Find its final velocity.

Solution:

Using v = u + at,

v = 0 + (3 × 4) = 12 m/s

Work, Energy, and Power

These quantities are fundamental to understanding mechanical processes.

Work (W): W = F × d (where F = force, d = distance).
Kinetic Energy (KE): KE = 0.5 × m × v²
Potential Energy (PE): PE = m × g × h (where g = 9.8 m/s², h = height).
Power (P): P = W / t (where t = time).

Example: Find the work done in moving a 5 kg object over 10 meters with a force of 20 N.

Solution:

Using W = F × d,

W = 20 × 10 = 200 J

2. Electromagnetism Formulas

Coulomb's Law

This law describes the electrostatic force between two charged particles.

F = k × (q₁ × q₂) / r²

Where k is the electrostatic constant (8.99 × 10⁹ N m²/C²), q₁ and q₂ are charges, and r is the distance between charges.

Example: Calculate the force between two charges of 3 C and 4 C separated by 2 meters.

Solution:

Using F = k × (q₁ × q₂) / r²,

F = 8.99 × 10⁹ × (3 × 4) / 2² = 26.97 × 10⁹ N

Ohm's Law

Ohm's Law relates voltage (V), current (I), and resistance (R).

V = I × R

Example: If the current is 2 A through a resistor of 5 Ω, find the voltage.

Solution:

Using V = I × R,

V = 2 × 5 = 10 V

Magnetic Force

The magnetic force on a moving charge in a magnetic field is given by:

F = q × v × B × sinθ

Where q is charge, v is velocity, B is magnetic field strength, and θ is the angle between v and B.

Example: Calculate the force on a 1 C charge moving at 3 m/s perpendicular to a 5 T magnetic field.

Solution:

Using F = q × v × B × sinθ with θ = 90° (sinθ = 1),

F = 1 × 3 × 5 = 15 N

3. Optics Formulas

Lens Formula

The lens formula relates the focal length (f), object distance (u), and image distance (v).

1/f = 1/v - 1/u

Example: Calculate the image distance for an object 30 cm from a lens with a focal length of 10 cm.

Solution:

Using 1/f = 1/v - 1/u,

1/10 = 1/v - 1/30

Simplifying, v = 15 cm

Snell's Law

This law describes the bending of light as it passes through different media.

n₁ sinθ₁ = n₂ sinθ₂

Where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction.

Example: Calculate the angle of refraction if light passes from air (n = 1) to glass (n = 1.5) at an incidence angle of 30°.

Solution:

Using n₁ sinθ₁ = n₂ sinθ₂,

1 × sin(30°) = 1.5 × sinθ₂

θ₂ ≈ 19.47°

Applications of Physics Formulas in Real Life

These physics formulas are foundational for understanding real-world phenomena and are applied in various fields such as engineering, technology, medicine, and environmental science. For example, Newton's laws are used in vehicle design, Coulomb's law in electronics, and optics principles in camera lenses.

Conclusion

Understanding physics formulas is essential for matriculation exams and provides a foundation for advanced study in physics. With these formulas, students can solve problems across mechanics, electromagnetism, and optics, building a strong base for further scientific exploration. Practice regularly with these formulas to improve your problem-solving skills and gain confidence in applying physics concepts to real-world scenarios.