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Free Fall Meaning
Free fall refers to the motion of an object under the sole influence of gravity, without any other forces acting on it. In free fall, all objects experience the same acceleration due to gravity (g), which is approximately 9.8 m/s² near the surface of the Earth. This acceleration acts downwards, towards the center of the Earth.
Formula for Free Fall
The primary formula for free fall is derived from the equations of motion under constant acceleration due to gravity (g). The standard value of gravitational acceleration on Earth is approximately 9.8 m/s2. The key equations are:
Velocity after a certain time (v):
v = g · t
Distance fallen after a certain time (d):
d = ½ · g · t2
Velocity after falling a certain distance (v):
v = √(2 · g · d)
Meaning of Variables
- Distance (d): It represents the vertical distance traveled by the falling object. The unit of distance can be meters (m) or any other suitable unit of length.
- Acceleration due to Gravity (g): It is the constant acceleration experienced by objects in free fall due to the gravitational force. The unit of acceleration is meters per second squared (m/s²).
- Time (t): It refers to the duration of the free fall, measured in seconds (s).
Assumptions for Free Fall Formula
The formula for free fall assumes that the object starts from rest (initial velocity u = 0) and is only influenced by the gravitational force. It neglects factors such as air resistance, the rotation of the Earth, and the variation of gravity with altitude.
Consistent units need to be applied when applying the formula and consider the direction of motion (positive or negative) based on the chosen reference frame.
Derivation of Free Fall Formula
Assumptions and Definitions
- Initial velocity (u): The initial velocity of the object. For free fall, this is typically u = 0 if the object is dropped from rest.
- Acceleration due to gravity (g): This is the constant acceleration acting on the object due to gravity, approximately 9.8 m/s2 near the Earth’s surface.
- Time (t): The time for which the object has been falling.
- Displacement (s): The vertical distance the object has fallen.
- Final velocity (v): The velocity of the object at time t.
Equations of Motion
The equations of motion for an object under constant acceleration are:
For free fall, the acceleration a is replaced by g (acceleration due to gravity), and the initial velocity u is often zero if the object is dropped from rest.
Derivation Steps
1. Velocity After Time t
From the first equation of motion:
If the initial velocity u = 0:
2. Displacement After Time t
From the second equation of motion:
If the initial velocity u = 0:
3. Velocity-Displacement Relationship
From the third equation of motion:
If the initial velocity u = 0:
Applications of Free Fall Formula
The free fall formula is often used to calculate the distance fallen or the time of fall for objects dropped or thrown vertically. It helps determine the vertical motion of objects in scenarios such as objects falling from a height, projectiles launched vertically, or bodies dropped into a well.
Understanding the free fall formula allows us to analyze and predict the motion of objects in the absence of other forces, providing valuable insights into various physical phenomena and practical applications.
Solved Examples to Understand Free Fall Formula
Example 1: A stone is dropped from a tall building. How far does it fall in 3 seconds?
Solution:
Given:
Time of fall (t) = 3 seconds.
Using the free fall formula: d = (1/2) x g x t²
Substituting the given values: d = (1/2) x 9.8 x (3)²
d = 4.9 x 9
d = 44.1 meters
Therefore, the stone falls approximately 44.1 meters in 3 seconds.
Example 2: An object is released from rest and falls freely for 2 seconds. What is its final velocity?
Solution:
Given:
Time of fall (t) = 2 seconds
Acceleration due to gravity (g) = 9.8 m/s².
Using the free fall formula to calculate the distance fallen: d = (1/2)x g x t²
Substituting the given values:
d = (1/2) x 9.8 x (2)²
d = 4.9 x 4
d = 19.6 meters
Now, we can calculate the final velocity (v) using the formula:
v = gt
Substituting the value of g and t:
v = 9.8 x 2
v = 19.6 m/s
Therefore, the final velocity of the object after 2 seconds of free fall is 19.6 m/s.
Example 3: A ball is dropped from a height of 25 meters. How long does it take to reach the ground?
Solution:
Given:
Distance fallen (d) = 25 meters,
Acceleration due to gravity (g) = 9.8 m/s².
Using the free fall formula: d = (1/2) x g x t²
Rearranging the formula to solve for time (t): t² = (2d) / g
t = √((2d) / g)
Substituting the given values:
t = √((2 x 25) / 9.8)
t ≈ √(50 / 9.8)
t ≈ √5.1
t ≈ 2.26 seconds
Therefore, it takes approximately 2.26 seconds for the ball to reach the ground when dropped from a height of 25 meters.
Frequently Asked Questions on Free Fall Formula
What is free fall method?
Free fall is when an object falls only under the influence of gravity, without any other forces acting on it, like air resistance. It means the object is falling freely towards the Earth.
What is the SI unit of free fall?
The SI unit for measuring the distance an object falls during free fall is meters (m). The acceleration due to gravity in free fall is measured in meters per second squared (m/s²).
What is called free fall?
Free fall is when an object is falling towards the ground with only gravity acting on it. There are no other forces, like air resistance, slowing it down.
What is the second equation of free fall?
The second equation of free fall is: s = 1/2gt^2 This equation tells us the distance (s) an object falls in time (t), with g represents the acceleration due to gravity (9.8 m/s² on Earth).
What is the best example of free fall?
A great example of free fall is when you drop a ball from a height, and it falls straight down without any push or resistance, only influenced by gravity.
