Grade 10 → Mechanics → Dynamics ↓
Free fall and acceleration due to gravity
Dynamics is the branch of physics that deals with motion, and one of the interesting motions to study is free fall. This phenomenon involves objects moving under the influence of gravity, and it is a concept that fascinates many people due to its simplicity and natural occurrence in our daily lives.
Understanding free fall
Free fall is a type of motion in which an object is subject only to gravity. This means that there are no other significant forces acting on it, such as air resistance. When you drop an object off a building, it often undergoes free fall, especially if the height is not so high that air resistance accumulates significantly.
Basic concepts of free fall
Here's a basic description of what happens during free fall:
- The object starts with an initial velocity. If it is dropped from rest, this velocity becomes zero.
- Gravity is the only force acting on the object.
- The object accelerates downwards at a constant rate, known as the acceleration due to gravity.
Acceleration due to gravity
Acceleration due to gravity is represented by the symbol g
. At the surface of the Earth, the value of g
is approximately 9.8 , text{m/s}^2
. This value means that, neglecting air resistance, the speed of a freely falling object will increase by approximately 9.8 , text{m/s}
every second.
Formula for velocity in free fall
The velocity of an object in free fall at any time can be calculated using the following formula:
V = U + GT
Where:
v
= final velocityu
= initial velocity (usually 0 if starting from rest)g
= acceleration due to gravity (9.8 , text{m/s}^2
)t
= time of falling of the object
Determining the fallen distance
The distance fallen by an object during free fall can be calculated using this formula:
s = ut + frac{1}{2}gt^2
Where:
s
= distance travelledu
= initial velocity (again, usually 0)t
= time of falling of the objectg
= acceleration due to gravity
Example: a falling apple
Let's consider a practical example. Imagine an apple falling from a tree. If it falls from a height of 5 m, we can calculate how long it will take for it to fall to the ground, ignoring air resistance.
Given:
- Initial velocity,
u = 0 , text{m/s}
- Height of fall,
s = 5 , text{m}
- Acceleration due to gravity,
g = 9.8 , text{m/s}^2
Using s = ut + 0.5gt^2
:
5 = 0 cdot t + 0.5 times 9.8 times t^2 5 = 4.9t^2 t^2 = frac{5}{4.9} t^2 approx 1.02 T approx sqrt{1.02} t approx 1.01 , text{s}
It takes about 1.01
seconds for the apple to fall to the ground.
Effects of air resistance
In the real world, air resistance can have a significant effect on the speed of falling objects. For example, a feather falls much slower than an apple because it is more affected by the air. However, by considering an ideal world (without air resistance), we gain insight into the fundamental principles of physics.
Comparing heavy and light objects
According to Galileo's law of falling bodies, if two objects are dropped from the same height, they will fall to the ground at the same time, regardless of their masses, provided there is no air resistance. This means that if you drop a hammer and a feather in a vacuum, they fall at the same rate.
Historical context
Galileo Galilei was one of the first people to challenge Aristotle's belief that heavier objects fall faster than lighter ones. His experiments at the Leaning Tower of Pisa were more anecdotal, but they served as a turning point in the understanding of free fall and gravity.
Newton and gravity
Isaac Newton's work built on earlier theories. He formulated the universal law of gravitation, which helped establish the mathematical principles needed to accurately describe free fall. His work explains why objects move the way they do, and how gravity acts as a force.
Practical applications
Understanding free fall is not just academic; it has practical implications in a variety of fields:
- Engineering: Designing structures that can withstand gravitational forces.
- Aeronautics: Making parachutes and understanding the motion of freely falling bodies.
- Sports: Analyzing the trajectories of balls and other sports equipment.
Example: skydiving
Skydivers experience free fall when they jump from an airplane. Despite initially accelerating due to gravity, they eventually reach terminal velocity, where air resistance balances the force of gravity, and they fall at a constant speed.
Conclusion
Free fall and acceleration due to gravity are fundamental concepts in physics that describe motion under the influence of gravitational forces. This understanding provides insight into natural phenomena and aids in the development of technology and innovations in various fields.
By exploring the math and physics behind free fall, students gain a deeper understanding of the laws that govern motion on Earth and beyond. Exploring these concepts forms the cornerstone in the study of mechanics and prepares students for more advanced topics in physics.