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 ↓


Free fall and terminal velocity


Introduction to free fall

The concept of free fall is pretty straightforward: it's a type of motion where an object is only affected by gravity, meaning no other forces like air resistance affect its motion. When we think of free fall in its purest form, we imagine it taking place in a vacuum where gravity is the only force.

Understanding gravity

Gravity is a force that pulls objects toward the center of the Earth. This is why when you throw an object up it comes back down. The force of gravity on an object located at or near the Earth's surface is approximately constant and its magnitude is represented by the symbol g. Its value is approximately 9.8 m/s^2.

Free fall speed

In free fall, because gravity is the only active force, all objects will experience the same acceleration due to gravity, regardless of their mass. This may seem paradoxical because we often see heavier objects falling faster in the presence of air resistance. But in a vacuum, where no air is present to slow anything down, a feather and a hammer will fall at the same rate.

Mathematical representation

Using the laws of dynamics, we can represent the free fall motion by the following equation:

V = GT

Where:

  • v is the final velocity of the object.
  • g is the acceleration due to gravity, which on Earth is about 9.8 m/s^2.
  • t is the time during which the object continued to fall.

An example of this would be calculating the velocity of an object after it has been in free fall for 5 seconds:

v = (9.8 m/s^2) times (5 s) = 49 m/s

This means that after 5 seconds, the object is moving downwards at a speed of 49 meters per second.

Distance covered in free fall

The distance fallen by an object during free fall can be calculated using this formula:

d = frac{1}{2} gt^2

Where:

  • d is the distance dropped.
  • g is the acceleration due to gravity.
  • t is autumn time.

Let's find how far an object falls in 5 seconds:

d = frac{1}{2} times 9.8 times 5^2 = 122.5  m

This calculation shows that the object will fall a distance of 122.5 meters in 5 seconds.

Free fall fantasy

Start After 1s After 2s Direction of motion

The figure above shows the trajectory of an object in free fall. Gravity pulls it straight towards the center of the Earth.

Introduction to terminal velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches, when the resistance of the medium through which it is falling prevents further acceleration.

When an object falls in air (or any other fluid), it experiences a drag force opposite to the direction of its motion. This drag force depends on many factors, including the size, shape, and velocity of the object, as well as the viscosity of the medium.

The concept of terminal velocity

As an object falls, its speed increases, which also increases the drag force acting on it. Eventually, this drag force becomes equal to the force of gravity acting on the object. When these two forces balance out, the object's acceleration stops and it falls at a constant speed called terminal velocity.

Mathematical description

The resistance force F_d acting on an object can be represented as:

F_d = frac{1}{2} C rho A v^2

Where:

  • C is the drag coefficient, which depends on the shape of the object
  • rho is the density of the fluid through which the object is moving
  • A is the cross-sectional area of the object
  • v is the velocity of the object

At terminal velocity, the following equation is true:

mg = frac{1}{2} c rho a v^2_t

where v_t is the terminal velocity, and mg is the weight of the object.

Example of terminal velocity calculation

Suppose a skydiver is jumping from an airplane. The skydiver's mass is 80 kg, the cross-sectional area is 0.7 m^2, the drag coefficient for the spread-eagle position is 1.0, and the air density is 1.225 kg/m^3.

We can find the terminal velocity using the balanced force equation:

mg = frac{1}{2} c rho a v^2_t

80 times 9.8 = frac{1}{2} times 1.0 times 1.225 times 0.7 times v^2_t

Solving for v_t, we get:

784 = 0.4285v^2_t
v^2_t = frac{784}{0.4285} approx 1832.9 
v_t approx 42.82  m/s

Thus, the terminal velocity for this skydiver is about 42.82 meters per second.

Visual exploration of terminal velocity

Start Descent Increasing the speed Terminal velocity

This visualization shows the process. The object first accelerates and then moves at a constant speed to terminal velocity due to balanced forces.

Factors affecting terminal velocity

  • Shape of the object: Most aerodynamic objects have a low coefficient of drag, resulting in a high terminal velocity.
  • Cross-sectional area: Larger area increases resistance, which reduces terminal velocity.
  • Altitude: At higher altitudes the resistance decreases due to lower air density, thus increasing the terminal velocity.
  • Mass: Heavier objects have a greater gravitational force, which increases the terminal velocity.

Conclusion

Understanding the concepts of free fall and terminal velocity provides information about the motion of objects under the influence of resisting forces such as gravity and air resistance. Free fall allows us to see how gravity naturally affects motion, while terminal velocity demonstrates the balance of forces in a fluid medium.

These principles are applied in a number of real-world situations, from the design of parachutes to predicting the fall rate of various objects, ensuring safety and efficiency in a variety of fields.


Grade 11 → 1.1.8


U
username
0%
completed in Grade 11

← Prev (1.1.7)
Equations of motion (advanced derivations)
Next (1.1.9) →
Projectile motion

Comments 



Free fall and terminal velocity

https://www.physicsflow.com/g11/1.1.8?pfal=en