An object at rest has stored energy, which transforms into kinetic energy when it moves. Motion is classified into 1-D (along one coordinate, like a boy cycling in a straight line), 2-D (along two coordinates, like children running in different directions), and 3-D (in all three coordinates, like an airplane). Special types of motion, such as circular, parabolic, and free fall, are subsets of 1-D or 2-D motion. Understanding 1-D motion is key to grasping the basics of movement.
What is Free fall?
Free fall of an object is defined as the time when the object is only under the influence of the force of gravity, and no other force is acting upon it. In real life, an object, when it undergoes free fall, also experiences other forces like air friction, etc.
Hence, it will not be considered a Free Fall. Instances of Free fall can be the moon revolving around the around the sun, as it only experiences the gravitational force from the sun, causing it to move in an elliptical orbit.
Free Fall Formula
Consider an object falling freely for a time t seconds, reaching a final velocity v from a height h, under the influence of gravity g. The motion of the object can be described by the following equations of motion:
- h= 1/2gt2
- v²= 2gh
- v=gt
Where,
h= Height traveled
v= Final velocity
g= Acceleration due to gravity
t= Time taken
These equations can be derived from the standard equations of motion given below by substituting:
- Initial velocity u=0,
- Distance traveled s=h and
- Acceleration a=g.
Derivation of Free Fall Formula
First Equation of motion
Since, during Free fall, the initial velocity of the object is 0m/sec and the acceleration acted upon is the acceleration due to gravity (g= 9.8 m/sec2). the equation will look like,
v= u+ at
u=0m/sec, a=g= 9.8m/sec2
v = gt
Second Equation of motion
As mentioned above, the second equation of motion under free fall shall be,
S = ut+ 1/2(at2)
S = H, u=0m/sec, a= g= 9.8 m/sec2
H = 1/2(gt2)
Third Equation of motion
The third equation of motion under free fall,
v2 = u2+ 2aS
S= H, u=0m/sec, a= g= 9.8m/sec2
v2 = 2gH
Table to show the Final Velocities, distance covered, in every second of a Free Fall,
Time (in seconds) | 0 | 1 | 2 | 3 | 4 | 5 |
Acceleration (in m/sec2) | 9.8 | 9.8 | 9.8 | 9.8 | 9.8 | 9.8 |
distance (in meters) | 0 | 4.9 | 19.6 | 44.1 | 78.4 | 122.5 |
velocity (in m/sec) | 0 | 9.8 | 19.6 | 29.4 | 39.2 | 49 |
Freefall is the natural phenomenon of a body with mass falling under its own weight. It depends solely on the height from the surface and the duration of the fall.
Motion in a Straight Line
- A body traveling in a straight line and in one direction has motion in a straight line.
- Examples include a car moving in a straight line or an object free-falling.
- The body is known to have uniform motion in a straight line if it travels an equal distance in per unit time. For example, if a car travels 3 meters every second, it is covering an equal distance every second; the speed of the body is 3m/sec.
- The other case can be having uniform acceleration, in this case, the body has constant acceleration, the speed changes uniformly.
- The body/object is known to have non-uniform motion in a straight line if it travels unequal distances in equal intervals of time. For example, A car traveling 2 meters for the first second and 3 meters for the next second.
Also Check,
- What is Gravity
- Gravitational Force
- Real life applications of Gravitational Energy
- Gravitational Potential Energy
- Value of Gravitational Constant
- Free Fall
- Solving Problems Based On Free Fall
Solved Examples
What happens when an object undergoes free fall?
When an object undergoes free fall, it starts with zero initial velocity, and keeps on increasing its velocity with a rate of 9.8 m/sec, hence, it experiences an acceleration of 9.8 m/sec2 which is also known as acceleration due to gravity.
What is the final velocity of the ball if it is dropped from a certain height and takes 10 seconds to reach the ground. The air resistance is not taken into account. [take g= 10 m/sec2]
Applying first equation of motion under free fall,
u= 0m/sec, S=H, a= g= 10m/sec2 (given)
v= u+ at
v= gt
v= 10× 10
v= 100m/sec
Rohan dropped his ball from a height of 5 meters and then he ran downstairs really fast to see if he can catch the ball, he takes 1 minute to reach the ground. Will he be able to catch the ball, please note that the air friction is neglected.
Applying second equation of motion under free fall,
S= ut+ 1/2(at2)
u=0 m/sec, a= g= 9.8m/sec2, S=H
H= 1/2(gt2)
5= 1/2(9.8× t2)
t2= 10/9.8
t= 1.01 second
As it is very clear that Rohan takes 1 whole minute to reach the ground while the ball reaches the ground in 1.01 second. Hence, there is no way he will be able to catch the ball.
If an object undergoes Free fall, what will be the velocity of the object on the 10th second?
Applying first equation of motion under free fall,
v= g.t
v= 9.8× 10
v= 98m/sec
Therefore, on the 10th second, the velocity of the object will be 98m/sec.
Find the height from which a toy is dropped, if it goes in free fall state and the final velocity achieved by the toy is 20m/sec.
Applying third equation of motion,
v2= u2+ 2aS
Under free fall,
u= 0m/sec, a= g= 9.8m/sec2, S=H
v2= 2gH
202= 2× 9.8× H
400 = 19.6× H
H= 20.40 meters.
What is the formula for free fall?
The formula for velocity in free fall is v=gt. Therefore, velocity is independent of the object's mass or weight.
How to calculate free fall force?
The force of free fall can be calculated using F=mg, where m is the mass of the object and g is the acceleration due to gravity.
What is free fall in physics class 11?
In physics, free fall refers to the motion of an object under the influence of gravity alone, with no other forces acting on it.
What is the SI unit of free fall?
The SI unit of free fall is meters per second squared (m/s²), which represents the acceleration due to gravity.
What is the gravity formula?
The formula for gravity is , F= Gm1m2/ r2 where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of two objects, and r is the distance between their centers.
Practice Questions
1. Imagine you drop a ball from the top of a building. How long would it take for the ball to reach the ground if the building is 50 meters tall? (Assume there's no wind resistance and gravity pulls the ball down at a constant rate).
2. A ball is dropped from a certain height. If it reaches a final velocity of 15 m/s just before hitting the ground, what is the height from which it was dropped? (Assume there is no air resistance and gravity is 9.8 m/s²).
3. A stone is dropped from a height, and it takes 8 seconds to hit the ground. If air resistance is ignored and g = 10m/ s² , what is the final velocity of the stone just before it hits the ground?