Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Mechanics → Dynamics ↓


Conservation of momentum


In physics, it is fundamental to understand how objects behave when they collide or interact with each other. One of the key principles that helps explain these behaviors is called "conservation of momentum." Let's take a deeper look at this principle to understand what it means, how it applies in different situations, and why it is so important in the study of dynamics in mechanics.

What is speed?

Before we discuss conservation of momentum, it is important to understand what momentum means. Momentum is a measure of the speed of an object. It is a vector quantity, which means it has both magnitude and direction. The momentum of an object can be calculated using the formula:

p = m × v

where p is momentum, m is mass, and v is velocity.

For example, if a car with a mass of 1000 kg is traveling east at a velocity of 10 meters per second, its momentum is:

p = 1000 kg × 10 m/s = 10000 kg·m/s

This means that the momentum of the car moving east is 10000 kg m/s.

Principle of conservation of momentum

The principle of conservation of momentum states that the total momentum of a closed system remains constant, provided no external forces act on it. This means that within a closed system, momentum can be transferred from one object to another, but the total amount of momentum remains the same.

Mathematically, momentum conservation can be expressed as:

p_initial = p_final

where p_initial is the total initial momentum of the system, and p_final is the total final momentum.

Visual example: collision of two balls

Imagine we have two balls on a flat surface. Ball A is moving towards ball B, which is initially stationary:

Let us understand this scenario:

  • The mass of ball A is 2 kg and it is moving at a velocity of 3 m/s.
  • Ball B has a mass of 3 kg and is initially at rest, so its velocity is 0 m/s.

The initial momentum p A of ball A is:

p A = 2 kg × 3 m/s = 6 kg·m/s

The initial momentum p B of ball B is:

p B = 3 kg × 0 m/s = 0 kg·m/s

The total initial momentum of the system is:

p_initial = p A + p B = 6 kg·m/s + 0 kg·m/s = 6 kg·m/s

Now, when ball A collides with ball B, ball A stops, and ball B starts moving with the full momentum of ball A.

Therefore, the final momentum of the system is still:

p_final = 6 kg·m/s

This shows conservation of momentum because the total momentum remains the same before and after the collision.

Another textual example: rocket propulsion

Conservation of momentum isn't just limited to balls colliding or cars crashing. It also applies to the motion of rockets. When a rocket moves through space, it relies on conservation of momentum to keep moving forward. This is how it works:

The rocket expels gas from its engine at high speed. The ejected gas has a certain momentum. To conserve momentum, the rocket itself must acquire an equal and opposite momentum.

  • If the mass of the expelled gas is m g and its velocity is v g, then its momentum is p g = m g × v g.
  • If the mass of the rocket is m r and it attains velocity v r, then its momentum is p r = m r × v r.

According to conservation of momentum:

|p g | = |p r |

This means that the momentum gained by the rocket is equal to the momentum of the expelled gas, but in the opposite direction, which makes the rocket move forward.

Impulse and its relation to momentum

Impulse is another important concept related to momentum. It is the change in the momentum of an object when a force is applied over a certain time period. The formula for impulse (J) is:

J = F × Δt

Where F is the force and Δt is the time period during which the force acts. The equation for impulse can also be expressed in terms of momentum:

J = Δp

This implies that impulse is equal to a change in momentum. So, if you apply a force to an object for a certain amount of time, you change its momentum. This relationship sheds further light on how force and momentum are interrelated through momentum.

Example of impulse with a soccer ball

Suppose a soccer ball is initially at rest. A player kicks the ball, and applies a force for a short time. Let's use numbers to visualize this:

  • The mass of the soccer ball is 0.45 kg.
  • The player applies a force of 45 N for 0.1 sec.

The impulse provided is as follows:

J = F × Δt = 45 N × 0.1 s = 4.5 N·s

The change in the ball's momentum, Δp, is equal to the impulse:

Δp = J = 4.5 N·s

Since the ball starts moving from rest, its initial momentum is zero, so the final momentum becomes 4.5 N s.

Conservation of momentum in a system of particles

When analyzing a system of particles, conservation of momentum extends to the collective system. The total momentum of the entire system remains the same before and after any interaction, provided that no external forces act on the system. Let's see how this happens with an example involving two skaters on ice:

Example: Ice skaters pushing each other

Imagine two ice skaters standing still on the ice. They push each other away. Skater A has a mass of 50 kg, and skater B has a mass of 70 kg. After the push, skater A moves backward at a velocity of 2 m/s. What is the resultant velocity of skater B?

Before they push each other their momentum is zero because they are initially at rest:

p_initial = 0

Their momentum after the push is obtained by summing their individual momenta:

p_final = p A + p B

Calculate the speed of skater A:

p A = 50 kg × 2 m/s = 100 kg·m/s

Let the velocity of skater B be v B Then the momentum of skater B is:

p B = 70 kg × v B

Use of principle of conservation of momentum:

0 = 100 kg·m/s - 70 kg × v B

Solving for v B gives:

v B = 1.43 m/s

Skater B moves in the opposite direction at a velocity of 1.43 m/s.

Understanding external forces and conservation of momentum

It is important to note that conservation of momentum is only true in the absence of external forces. External forces such as friction, air resistance, or any external influence can change the total momentum of a system. Therefore, exercises and problems dealing with momentum conservation often specify "in a closed, isolated system" because it is assumed that no external forces are acting on the objects.

Conclusion

Conservation of momentum is a fundamental concept in physics that helps us understand the behavior of moving objects when they collide with each other. Whether it's a car collision, a spacecraft entering orbit, or a simple ball game, the principles of momentum provide valuable information about what will happen next and why. By applying the law of conservation of momentum, physicists and engineers can predict outcomes in scenarios where objects collide or are pushed apart - a foundational skill in designing everything from vehicles to safety equipment.

This principle ensures that in a closed system—with no external forces—the cumulative amount of momentum remains unchanged despite interactions between objects inside the system.


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Conservation of momentum

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