Mechanics: Free Fall

Mechanics: Free Fall

Basic Principles

  • Free fall is the motion of an object under the influence of gravity alone, with no other forces acting on it.
  • All objects in free fall near the Earth’s surface experience a constant acceleration due to gravity (g), which is approximately 9.81 m/s² downwards.
  • This principle applies regardless of the object’s mass. This is known as the principle of equivalence.
  • The velocity of an object in free fall increases linearly with time, provided air resistance is negligible.

Equations of Motion

  • The three basic equations of motion apply to free fall scenarios:
    • v = u + at : final speed equals initial speed plus acceleration times time.
    • s = ut + 0.5at² : Displacement equals initial speed times time plus half of acceleration times time squared.
    • v² = u² + 2as : Final speed squared equals initial speed squared plus 2 times acceleration times displacement.
  • In these equations, a is the acceleration due to gravity, t is the time, v is the final velocity, u is the initial velocity, and s is the displacement or height.
  • Be aware that the displacement s, may be negative if the object is moving downwards.

Upwards and Downwards Motion

  • If an object is projected upwards and then falls back down, the upward and downward paths are symmetrical - the object spends the same amount of time rising as it does falling.
  • The object’s speed when it returns to its starting height is the same speed it was launched with (ignoring air resistance).
  • The total time in the air (flight time) can be found using the equation t = 2u / g.

Air Resistance and Terminal Velocity

  • In the real world, air resistance affects free fall motion. It acts against the motion of falling objects and increases with speed, until a constant speed known as the terminal velocity is reached.
  • The terminal velocity is the speed at which the force due to gravity is balanced by the air resistance, and the object no longer accelerates.
  • This requires a knowledge of forces and dynamics, and use of Newton’s second law, F = ma, where forces (like air resistance and gravity) are balanced.

Applications and Examples

  • Free fall principles apply to many scenarios like dropping a stone from a cliff, a parachutist jumping from a plane before he opens his parachute, or a projectile fired vertically upwards.
  • When working out problems, always make sure to carefully define your coordinates and remember that up and down have opposite signs.

Advanced Topics

  • Free fall under the influence of gravity can also be regarded as a special case of motion in a gravitational field.
  • In space, where gravity can be much less than on Earth, or on other planets, the acceleration due to gravity g will be different.
  • These topics might be expanded upon in further physics or applied maths studies, taking into account factors like the rotation of the Earth, altitude above sea level, or space travel.