4.8 • +11k Ratings
Save
Print
Edit
You must have heard the phrase ‘what goes up must come down’. In physics terms, as Sir Isaac Newton discovered, what goes away from the earth will be pushed back towards it. So, when you throw a ball in the air, whether it goes straight up, to the left, or to the right, it eventually falls back to the ground. And this is true regardless of the height from which the ball is released.
In fact, it takes a significant amount of force, such as the engines of an aeroplane and the lift force produced by the wings, to keep pushing an object away from the earth. Without these forces, it would fall out of the sky.
Gravity is a force that attracts all objects that have a mass to each other. As the earth has a mass, it attracts other objects towards it. The same is true for other objects, which similarly attract each other towards themselves, including the earth. Even we attract the earth towards ourselves with the force of gravity.
But why isn’t this obvious? Why don’t we see other objects attract each other, given that they all have mass? We will consider this in what follows.
A force field is a region in which an object experiences a non-contact force.
Force fields cause an interaction between objects and particles without the objects touching each other. In the case of gravity, that interaction happens between masses. Any object will experience an attractive force if you put it in the gravitational field of another object.
Force fields can be represented as a system of vectors, as in this diagram, in which the arrows represent the gravitational field on the earth.
Figure 1. Gravitational field lines. Source: Sjlegg, Wikimedia Commons (Public domain).
The earth’s gravitational field is radial, which means that the lines of force intersect at the centre of the earth.
As the diagram shows, the field lines are closer together at the surface of the earth. This indicates that the gravitational force is stronger here. Where the lines move further apart from each other, the force decreases.
Have a look at the equation below, which represents Newton’s law of gravitation:
= mass of one of the objects.
= mass of the other object.Newton’s gravitational field: when two bodies are placed in a gravitational field, they experience a force that is the product of the two masses and the inverse square of the distance from the centre of both masses.
The constant G is a gravitational constant, which has a very small value:
Calculate the gravitational force between two 3kg spheres that are 2m apart.
The mass of both objects is 3kg. So m1 and m2 are 3kg, while r is 2m, with G being 6.67 * 10 ^ -11 Nm ^ 2 / kg ^ 2. Putting in all the values gives us:
The gravitational constant G, which, as we said, has a very small value, is the reason why objects don’t fly and collide with each other. It is also the reason why the earth is not attracted to us but we to it. After all, our mass is negligible compared to that of the earth.
Figure 2. Force F acting on m2 due to m1. Source: Usama Adeel, StudySmarter.
The distance between the two objects has more impact than their masses because Newton’s gravitational equation follows an inverse square law. This means that if the distance doubles, the force is one-quarter of the strength of the original force.
The force of a single mass is its gravitational field strength, which is defined as force per unit mass when it is placed in a gravitational field.
).As the gravitational field on the earth’s surface is almost uniform, we can assume g to be constant. Hence, g is just the acceleration of mass m in a gravitational field.
Point masses are objects that behave as if all mass is concentrated at their centre. Uniform shapes have a point mass.
The significance of point masses is that they have a radial gravitational field. In this, the field lines radiate from its centre. For point masses, our earlier equation becomes:
).The gravitational force depends on the mass of the planet. Mars, for instance, has a gravitational field strength of 3.71 N/kg because it is only about half the diameter of the earth. But, and here comes the interesting part, your weight also depends on the gravitational force g.
Your mass is the same wherever you go in the universe. What differs is your weight, which depends not only on your mass but also on gravity. So, for instance, if you weigh 99.8kg on earth, you would only weigh 37.74kg on Mars.
The moon has a gravitational force of 1.62 N/kg. This is why on the moon, it is easier to fly than to walk. On Mars, walking becomes a bit easier but is still a challenge because of the low gravitational pull.
The tides that form on the surface of the earth show how both mass and distance affect the gravitational force.
We get tides on the earth’s surface because of the gravitational pull of the moon and the sun. And although the sun has far more mass than the earth, the distance between the two plays a significant role due to the inverse square proportionality. As the moon is much closer to the earth, the earth’s oceans respond to the moon revolving around the earth, which causes the tides. The sun does have an impact, too, but the tides produced by the sun are much smaller.
The law of gravitation is an inverse square law, which says that the gravitational force decreases when the distance between the objects increases.
Gravitational field strength is force per unit mass acting on an object placed in a gravitational field.
In a radial field, the gravitational field can be represented as:
The gravitational field strength on earth is 10 N/kg.
Gravitational field strength is calculated as follows:
g=F/m
It is measured in Newtons per kilogram (N/kg).
A gravitational field is a region where an object experiences a gravitational force due to the presence of another object.
This can be calculated using the equation below:
weight = mass * gravitational field strength
w=m*g
Be perfectly prepared on time with an individual plan.
Test your knowledge with gamified quizzes.
Create and find flashcards in record time.
Create beautiful notes faster than ever before.
Have all your study materials in one place.
Upload unlimited documents and save them online.
Identify your study strength and weaknesses.
Set individual study goals and earn points reaching them.
Stop procrastinating with our study reminders.
Earn points, unlock badges and level up while studying.
Create flashcards in notes completely automatically.
Create the most beautiful study materials using our templates.
Sign up to highlight and take notes. It’s 100% free.
