Why do things fall down? Why must we apply effort to make things go up? Do all things fall down at the same rate? Why do we not use an airplane to go to moon or outer space? So many questions. We will try to answer them in this article.
Things fall down due to Gravity
Gravity is defined as the force that pulls things down towards the earth’s centre. In the universe, all objects have gravitational force and pull each other. So, just as the earth pulls us towards itself, we too pull it towards ourselves. But due to the enormous difference in masses, the effect of our pull is negligible
Are Gravity and Force of Gravitation the same?
Yes and No.
By yes, it means that gravity is also an attracting force, just like gravitational. Then what is the difference?
Gravitation is the attractive force between two objects in space. Gravity is the gravitational force exerted by the earth on all objects on its surface. When we talk about gravity, it refers only to the earth.
Universal Law of Gravitation
Two bodies of mass m1 and m2 are is free space. The distance between their centres is d metres.
The universal law of gravitation states that these two bodies are attracted to each other by a force that is-
i. directly proportional to the product of their masses, and
ii. inversely proportional to the square of the distance d between their centres
Let us consider the mass of earth as M and an object with mass m.
G is called the universal gravitational constant. It is universal as it is applicable everywhere in the universe.
Acceleration due to Gravity
Acceleration due to gravity is the acceleration due to the force of gravitation of the earth. A parachutist jumping from an airplane falls freely for some time. He experiences an acceleration caused by the gravitational force of the earth.
The only force acting on a freely falling body is that of gravity. This force makes the things falling to increase velocity as it nears the surface. The velocity increases at a constant pace. Therefore, this acceleration is constant at all instants.
We define acceleration as the rate of change of velocity, or, change in velocity divided by time.
According to Newton’s Second Law of Motion, Force is the product of mass and acceleration.
F=mass x acceleration
F = ma
Acceleration of a freely falling body is acceleration due to gravity, and the symbol used is ‘g’ instead of ‘a’.
For gravitational force of the earth (gravity), F = mg
For an object falling towards the earth, the distance between it and the surface is negligible compared to the radius r of the earth. So, we can equate d to r.
This equation shows that acceleration due to gravity, g depends on the-
i. mass of the earth, M
ii. the radius of the earth, r
The mass of the object does not affect g. All objects fall at the same acceleration simultaneously from the same height, irrespective of their weights. This was demonstrated by the Italian astronomer and scientist, Galileo Galilei from the Leaning Tower of Pisa.
If a leaf or piece of paper falls slowly, it is because of air resistance to such light objects. A parachute uses air resistance to slow down the fall. In a vacuum with no air, a feather and a block of iron fall to the ground simultaneously.
Value of Acceleration due to Gravity
A freely falling body increases its velocity by 9.81 m/s every second as it nears the surface.
Variation in g due to the Shape of the Earth
The earth is not a perfect sphere but is bulged at the equator and slightly flattened at the poles. So, the value of g is somewhat more at the poles compared to the equator.
Acceleration due to gravity at the equator
Acceleration due to gravity at the poles
Since radius at equator is more than radius at poles, rq > rp, therefore, gp>gq. That is, acceleration due to gravity at the poles is more than that at the equator.
Escape Velocity
A ball thrown up goes up to some height and falls towards the earth. This is because of the low velocity with which it is thrown up. To move something out of the earth’s gravitational force, there is a minimum velocity needed for the object to escape from its pull.
Escape velocity is defined as the minimum velocity needed by an object to overcome the earth’s gravitational force.
The minimum velocity with which rockets can go out into space escaping the earth’s gravity is 11.205 km/s.
Mass and Weight - Are they same?
We use the terms mass and weight interchangeably in our daily lives. But in science, there is a difference between the two.
- Mass is the amount of matter in an object.
- It is a scalar.
- It remains constant throughout, and at all places.
- Mass can bever be zero.
- SI unit of mass is kilogram (kg).
Weight (W)
- Weight is the force by which the earth, or any large body, pulls an object towards itself.
- It is a vector.
- It changes according to the distance from the centre.
- Weight can be zero.
- SI unit of weight is newton (N).
Weight and mass are related by the equation, W = mg
Comparison of Weight on the Earth and on the Moon
The mass of the earth is approximately 100 times that of the moon. The radius of the earth is about 4 times that of the moon. Using this relation, and comparing the acceleration due to gravity of the earth and the moon, we get
We = 6.25 Wm
where We is the weight of an object on the earth, and Wm is its weight on the moon.
Came here by chance. Your site and blogs are informative. Good work!
Not just the post, but loved the animation video also. What software you used?
This is a topic that is near to my heart… Thank you! Where are your
contact details though?