Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Mechanics → Dynamics ↓


Momentum and Impulse


In the world of physics, we often talk about how things move and what makes them move. Two important concepts that help us understand motion are momentum and impulse. These concepts are part of the broader study of mechanics and help us describe, predict, and control motion in everyday life and advanced scientific applications. This article will discuss these topics in depth, explain in simple language, and provide plenty of examples and equations.

Motion

Momentum is a measure of the amount of motion an object has. If you've ever tried to catch a flying baseball or watched a car speed down the highway, you've already had some experience with the concept of momentum. In simple terms, it tells you how difficult it is to stop a moving object.

Understanding momentum

Momentum is a vector quantity, which means it has both magnitude and direction. The momentum of an object depends on two major factors:

  • What is the mass of the object (mass or m)
  • how fast it is moving (velocity or v)

The formula for momentum is:

p = m * v

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

Example: Rolling ball

Imagine a small ball with a mass of 2 kg moving at a speed of 3 m/s. The momentum of this ball can be measured as follows:

p = m * v = 2 kg * 3 m/s = 6 kg·m/s

Therefore, the momentum of the ball in the direction of motion is 6 kilogram metres per second.

Impulse

While momentum describes the motion of an object, impulse describes a change in that motion. Impulse can be thought of as the action that changes the motion of an object, whether it makes it move faster, slower, or changes its direction. In simple terms, impulse is the effect of a force applied over a period of time.

Understanding impulsivity

Impulse is also a vector quantity and is described using this formula:

Impulse = Force * Time

The standard unit of impulse is the newton-second (N s), which is equivalent to kg m/s. This is the same unit as momentum, highlighting the close connection between the two concepts.

Impulse-momentum theorem

The impulse-momentum theorem beautifully connects impulse to momentum. It states that the impulse applied to an object is equal to the change in the momentum of that object. Mathematically, it can be expressed as:

Impulse = Δp = m * Δv = F * Δt

Where Δp is the change in momentum, Δv is the change in velocity, F is the force, and Δt is the time interval during which the force acts.

Example: Hitting a soccer ball

Suppose a football player is kicking a stationary ball. Suppose a ball of mass 0.5 kg is kicked and given a speed of 10 m/s. The change in momentum of the ball is:

Δp = m * Δv = 0.5 kg * 10 m/s = 5 kg·m/s

If the player's foot exerts a force in 0.1 sec, then the average force applied will be:

F = Δp / Δt = 5 kg·m/s / 0.1 s = 50 N

Due to this force the velocity of the ball increased from 0 m/s to 10 m/s.

Conservation of momentum

An important principle in the study of momentum is conservation of momentum. This principle states that within a closed system (meaning there are no external forces acting on it), the total momentum before an interaction is equal to the total momentum after the interaction.

Example: Collision of two cars

Imagine two cars colliding. Car A has a mass of 1000 kg and moves at 15 m/s. Car B, which has a mass of 1500 kg, moves at 10 m/s toward car A. In a collision where the two cars are locked together, the principle of conservation of momentum allows us to calculate the combined momentum after the collision.

Car ACar B

The total initial momentum is:

p_initial = (m_A * v_A) + (m_B * v_B) = (1000 kg * 15 m/s) + (1500 kg * -10 m/s) = 15000 kg·m/s - 15000 kg·m/s = 0 kg·m/s

After the collision, the combined mass is 2500 kg. Therefore, the momentum v_f can be calculated from the conservation principle:

p_final = m_combined * v_f = 0 kg·m/s v_f = 0 kg·m/s / 2500 kg = 0 m/s

The cars do not move after the collision, which brings into effect the principle of conservation of momentum, since momentum remains constant.

Applications of momentum and impulse

Sports and athletics

In sports like football, understanding momentum helps players increase performance and avoid injuries. In ball games like basketball and soccer, impulse plays a vital role during passes and shots. A skilled player manages to control momentum and apply impulse judiciously.

Vehicle safety

Car safety systems, such as seatbelts and airbags, use the concept of impulse. By increasing the duration of the force generated by a collision, these systems reduce the force exerted on passengers, improving passenger safety.

Space mission

In space exploration, scientists apply the concepts of momentum and impulse to propel spacecraft. In the vacuum of space, expelling gas in one direction results in the spacecraft moving in the opposite direction (conservation of momentum).

Conclusion

The concepts of momentum and impulse are fundamental in understanding the dynamics of motion. They help explain everyday phenomena and guide engineers and scientists in many disciplines in designing systems that efficiently control or regulate motion. Through the principles of momentum conservation and the impulse-momentum relation, we gain powerful tools for describing and predicting the behavior of objects in motion.


Grade 11 → 1.2.8


U
username
0%
completed in Grade 11

← Prev (1.2.7)
Banking of roads and curves
Next (1.2.9) →
Conservation of momentum in one and two dimensions

Comments 



Momentum and Impulse

https://www.physicsflow.com/g11/1.2.8?pfal=en