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Free Fall

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Ordinary Differential Equations

Definition

Free fall refers to the motion of an object when it is falling solely under the influence of gravity, with no other forces acting on it. This means that the only force acting on the object is gravitational force, resulting in a uniform acceleration towards the Earth at approximately $$9.81 \, m/s^2$$. In free fall, all objects, regardless of their mass, experience the same acceleration, which highlights a fundamental principle of mechanics and motion problems.

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5 Must Know Facts For Your Next Test

  1. In a vacuum, all objects in free fall experience the same acceleration due to gravity, regardless of their mass or shape.
  2. The acceleration due to gravity near the Earth's surface is approximately $$9.81 \, m/s^2$$, which means that the speed of a falling object increases by this amount every second.
  3. Free fall can only occur when there are no other forces acting on the object, such as air resistance or friction.
  4. When an object reaches terminal velocity during free fall, it stops accelerating and continues to fall at a constant speed.
  5. In real-world scenarios, most falling objects do not experience true free fall due to air resistance, but they can approximate it over short distances.

Review Questions

  • How does free fall demonstrate the principles of acceleration and gravitational force in mechanics?
    • Free fall exemplifies how acceleration is directly influenced by gravitational force. When an object is in free fall, it accelerates uniformly at about $$9.81 \, m/s^2$$ because gravity is the only force acting on it. This consistent acceleration applies to all objects regardless of their mass, showcasing that gravitational force dictates motion in free fall scenarios.
  • Discuss how air resistance affects free fall and what happens when an object reaches terminal velocity.
    • Air resistance significantly impacts free fall by opposing the motion of falling objects. As an object accelerates downward due to gravity, air resistance increases until it equals the gravitational force acting on the object. At this point, the object stops accelerating and falls at a constant speed known as terminal velocity, where the forces of gravity and air resistance are balanced.
  • Evaluate the implications of free fall experiments conducted in a vacuum versus those conducted in Earth's atmosphere.
    • Experiments on free fall conducted in a vacuum reveal that all objects fall at the same rate regardless of their mass, underscoring the universality of gravitational acceleration. In contrast, experiments in Earth's atmosphere demonstrate that air resistance alters falling behavior, leading to variations in acceleration and final velocities among different objects. This comparison highlights how environmental factors can influence motion and deepen our understanding of basic physics principles.
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