A freely falling body is an object that is moving under the sole influence of gravity. This means that air resistance is negligible, and the only force acting on the object is the force of gravity.
Here's a breakdown of the motion of a freely falling body:
1. Uniform Acceleration:
* Acceleration due to gravity (g): The Earth's gravitational field exerts a constant acceleration on all objects near its surface. This acceleration is approximately 9.8 m/s², directed downwards.
* Constant acceleration: The acceleration due to gravity remains constant throughout the fall. This implies that the velocity of the object increases at a constant rate.
2. Velocity:
* Initial Velocity (v₀): The velocity of the object at the beginning of its fall. This can be zero if the object is dropped from rest, or it can have a non-zero value if the object is thrown downwards or upwards.
* Final Velocity (v): The velocity of the object at any given time during its fall. This is determined by the initial velocity and the time elapsed.
* Relationship between velocity, acceleration, and time: The final velocity (v) can be calculated using the following equation:
v = v₀ + gt
where:
* v₀ is the initial velocity
* g is the acceleration due to gravity
* t is the time elapsed
3. Displacement:
* Displacement: The change in position of the object during its fall. It is measured from the initial position to the final position.
* Relationship between displacement, initial velocity, time, and acceleration: The displacement (Δy) can be calculated using the following equation:
Δy = v₀t + (1/2)gt²
where:
* v₀ is the initial velocity
* g is the acceleration due to gravity
* t is the time elapsed
4. Equations of Motion:
The following are the four fundamental equations of motion for a freely falling body:
* v = v₀ + gt
* Δy = v₀t + (1/2)gt²
* v² = v₀² + 2gΔy
* Δy = (v + v₀)t/2
5. Air Resistance:
In reality, air resistance plays a significant role in the motion of falling objects. As an object falls, it experiences an upward force due to air resistance. This force increases with the object's velocity.
* Terminal Velocity: Eventually, the force of air resistance will equal the force of gravity. At this point, the object stops accelerating and reaches a constant velocity called terminal velocity.
Conclusion:
Understanding the motion of a freely falling body is fundamental to comprehending classical mechanics. These equations provide a framework for predicting and analyzing the motion of objects in a gravitational field. However, it's crucial to remember the limitations of these equations and consider the influence of air resistance in real-world scenarios.
