Free Fall and Motion Mechanics

Free Fall

• Free fall is uniformly accelerated motion under the sole influence of gravity
• Objectives for understanding free fall include: defining free fall, describing a free-falling object's behavior, characterizing free fall's three cases, deriving kinematic equations for free fall, and solving free fall problems

Predicting the motion

• A bowling ball and feather dropped simultaneously won't hit the ground at the same time in the presence of air resistance.
• The bowling ball will fall faster due to its lower air resistance compared to the larger surface area of the feather

Debunking Common Myths

• Heavier objects don't fall faster than lighter objects in a vacuum. Air resistance affects this outcome.
• Objects with larger surface areas experience higher air resistance, resulting in slower fall rates compared to objects with smaller surface areas.
• In a vacuum, objects of any mass fall at the same rate due to the absence of air resistance.

Key Features of a Free Falling Object

• Acceleration due to Gravity:

  • The only force acting on a free-falling object is gravity.
  • Acceleration due to gravity (g) is approximately 9.8 m/s².
  • Acceleration is directed downwards towards the Earth's center.

• Time Symmetry (for objects thrown upwards):

  • Time taken to reach the maximum height equals the time to return to the starting point.

• Speed Symmetry (for objects thrown upwards):

  • Speed of the object at any point on the way up equals the speed at the corresponding point on the way down, ignoring air resistance.

• Velocities (for objects thrown upwards):

  • Upward velocity is positive and decreasing.
  • Downward velocity is negative and increasing.

Kinematic Equations for Free Fall

• Kinematic equations for uniformly accelerated motion are adaptable to free fall, changing variables slightly.
• The following table summarizes free fall quantities and their notation:

Three Cases of Free Fall

• Object Dropped at a Certain Height:

  • Initial vertical velocity (Voy) = 0 m/s.

• Object Thrown Downward:

  • Non-zero negative initial velocity (i.e., Vo y< 0).

• Object Thrown Upward:

  • Non-zero positive initial velocity (i.e., Vo y> 0).

Sample Problems (Illustrative Examples)

• Various examples using equations of motion to calculate different values such as the time taken to fall, maximum height, and final velocity, depending on different starting conditions. Specific values to each example are included in notes (e.g., initial velocity, acceleration, height)