Tru Physics

Free Fall

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Tru Physics
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Free fall is the motion of an object under the influence of gravity alone, with no other forces acting upon it. In an idealized scenario, it’s assumed that there’s no air resistance, and the object falls under a constant gravitational acceleration. Free fall is an essential concept in classical mechanics and serves as a foundation for understanding more complex motion.

Key Concepts

  1. Gravitational acceleration: The acceleration due to gravity, usually denoted as g, is approximately 9.81 \frac{\text{m}}{\text{s}^2} near the Earth’s surface. The value of g can vary slightly depending on the location and altitude. It’s important to note that gravitational acceleration acts downward, towards the center of the Earth.
  2. Uniform acceleration: During free fall, an object experiences a constant acceleration, which simplifies the equations of motion.

Important Equations

  1. Position as a function of time: The vertical position y(t) of an object in free fall, given its initial position y_i and initial velocity v_i, can be calculated using the following equation: y(t) = y_i +v_i t - \frac{1}{2}gt^2
  2. Velocity as a function of time: The vertical velocity v(t) of an object in free fall, given its initial velocity v_0, is determined by: v(t) = v_i - gt
  3. Final velocity after a certain distance: The final velocity v_f of an object in free fall, given its initial velocity v_i and the distance it has fallen \Delta y, can be found using:v_f^2 = v_i^2 - 2g \Delta y

Note: The equations above all use g=9.81 \frac{\text{m}}{\text{s}^2}. This is a positive constant. The direction has already been accounted for by the minus signs in each equation.

Real-life Examples

  1. Skydiving: A skydiver experiences free fall (ignoring air resistance) as they jump out of an airplane, accelerating towards the Earth until they reach terminal velocity or deploy their parachute.
  2. Projectile motion: An object projected horizontally experiences free fall in the vertical direction, which determines its flight time and maximum height.
  3. Falling objects: Everyday objects dropped from a height, such as a book or a pen, experience free fall as they accelerate towards the ground.

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