In this lesson, we’re going to explore the effects of gravity on the Earth. First, we’ll talk about what gravity is, then we’ll have a look at Newton’s law of gravity. Next, we’ll look at the effects of gravity, and a type of motion called free fall. Finally, we’ll talk a little bit about projectile motion.
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Added on: 29th Sep 2018
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In this presentation we’re going to explore the effects of gravity on the Earth.
First, we’ll talk about what gravity is, then we’ll have a look at Newton’s law of gravity. Next, we’ll look at the effects of gravity, and a type of motion called free fall. Finally, we’ll talk a little bit about projectile motion.
If you have two objects, both of which have mass, then there’s a force between them that attracts them to each other. This force is called gravity. It isn’t very noticeable for small objects: because their masses are so small, the force is very weak. However, it is very noticeable for large objects like stars and planets. It’s just as well that this force exists: we could not live on the Earth if there was no gravity. In fact, our atmosphere could not stay surrounding the earth, so we could not breathe. We also could not walk around and remain on the surface of the earth, we’d go floating off into space.
Our old friend, Sir Isaac Newton, came up with a law for calculating the size of the gravitational force between two objects. It’s called Newton’s law of universal gravitation and it states that a particle in the universe attracts every other particle in the universe with a force that is directly proportional to the product of their masses (it increases as the masses increase) and inversely proportional to the square of the distance between them (it decreases as the distance increases). In the formula you can see on your screen, F_g is the gravitational force, G is a universal gravitational constant, m_1 and m_2 are the masses of the two objects, and r is the distance between them. You can see this force is really large for objects with large masses, and quite small for objects that are a long way apart.
Let’s just explore the consequences of the law of universal gravitation a little further. So, it tells us that if take any old two masses, from anywhere in the universe, they’re attracted to each other. This force is always there. However, the size of it varies. If the masses are heavier, the attractive force will be stronger, but as the distance between the masses becomes larger, the attractive force becomes weaker.
No matter where we go in the universe, our mass does not change, but our weight depends on the size of the force of gravity that is acting on us. The weight of a body is defined to be the force that gravity exerts on that body. This is often calculated using the formula W= mg, where W is the weight, m is the mass of the body and g is the acceleration due to gravity. We have a certain weight on the Earth caused by the gravitational attraction of the Earth. As we move away from the earth, our distance r from the earth increases, and our weight decreases according to Newton’s Law of Universal gravitation. If we go to another planet or the moon, our weight will change because there will be a different gravitational force on that planet, depending on the mass of that planet. So, the acceleration due to gravity will change, and our weight will change.
Different planets in our solar system have different masses, and so they provide different gravitational forces when we move to them. Suppose you weighed 50.5 kg on Earth. Let’s have a look at your weight on some of the other celestial bodies in our solar system. They’re listed in the table at the side of this slide. Notice how heavy you’d be on the Sun! That’s because our Sun has a mass that is many times larger than that of the Earth. Pluto is much lighter than the Earth, so our weight is much smaller on Pluto.
We’ve all seen video footage of astronauts floating around on the International Space Station and other space craft. They are experiencing weightlessness. As we move away from the surface of the Earth, the gravitational force becomes smaller and is negligible (essentially zero) once we reach a certain distance from the surface of the Earth. At this point, we say that the objects are “weightless” as there is no appreciable force of gravity acting on them. However, some scientists refer to this as “microgravity” as there is always a very small gravitational force acting. This is what our floating astronauts are experiencing when they are in space. Space craft generate artificial gravity to counter weightlessness. One way in which they do this is by spinning.
No matter where you stand on the Earth, gravity pulls you towards the centre of the Earth. The Earth really has no top or bottom, despite the way maps are drawn. Wherever you stand on Earth, you feel as if you are the right way up. No blood rushes to your head, and no-one falls off the Earth. What would happen if we dug a hole all the way through the Earth and fell into it? Would we fall right through the Earth? No, because gravity attracts us to the centre of the Earth. But we wouldn’t just go straight to the centre and stay there. One of Newton’s laws tells us that motion is resistant to change. This is called inertia. Our inertia would not allow us to stop at the centre of the Earth. Instead we would continue to move forward until the force of gravity overcame our inertia and pulled us back to the centre of the Earth. Then our inertia in that direction would take us back past the centre, and we’d be pulled back to the centre by gravity. We’d continue to bounce back and forth, close to the centre of the Earth, and getting closer, but never stopping, unless another force like friction acted to stop us.
Essentially the same gravitational force acts on every object on Earth because the Earth’s mass is so much larger than the masses of the other objects. It might appear that the Earth attracts heavier objects with a greater force than lighter objects. For example, a stone appears to fall more quickly than a feather. However, this is not because of gravity. This is because a different amount of a frictional force called air resistance acts on the stone and the feather because of their different shapes. More air resistance acts on the feather and slows it down. If there was no air resistance, then both the stone and the feather dropped at the same time would fall with the same speed and reach the ground at the same time.
Energy is the ability of an object to do work. The force of gravity can do work as it can cause objects to accelerate, but the amount of work down depends on the distance that the force can accelerate the object over. In other words, it depends on how high the object is above the surface of the earth. If an object lies on flat ground, then gravity can’t pull it down anywhere, so it cannot do work.
The energy stored in an object because of its position is called the object’s potential energy. A very important type of potential energy is gravitational potential energy. You guessed it, objects have gravitational energy because of gravity. The amount of gravitational potential energy possessed by an object depends on the height of the object above the surface of the earth, the mass of the object and the acceleration due to gravity. It is calculated by the formula
Potential Energy = mass times acceleration due to gravity times height.
As an object falls, some of its potential energy is converted to kinetic energy – the energy of movement. This kinetic energy can then be used to produce work. One important use for gravitational potential energy is in hydroelectric energy schemes, where electricity is produced using the potential energy of water. Water from rivers or canals is stored at a relatively high level in hydroelectric dams. It is then dropped from the height and the potential energy of the water is transformed into kinetic energy, which, in turn, is used to power turbines that run the generators that produce the electricity.
When parachutists jump out of planes, they are falling under the action of gravity only until they open their parachutes. This is called free fall motion. The speed of the object in free fall increases at every instant until it hits the ground (splat!). The rate of acceleration depends on the gravitational acceleration on the planet where the freefall is taking place. On Earth, the gravitational acceleration is 9.8 metres per second squared, so the speed of a free falling object increases by 9.8 metres per second every second.
Now, let’s talk about projectile motion for a while. This is the sort of motion you see when a canon ball is fired, or someone hits a golf ball or you throw a ball. We’ll start with the simplest form, which is when an object is dropped from a height. When an object is dropped from a certain height with some initial horizontal velocity, it follows a curved path. The object is called a projectile, and the curved path is the type of path taken by projectiles in motion. If you’ve seen parabolas in maths, the path looks like an upside down parabola. Don’t worry if you haven’t - it’s a type of curved path. The picture shows three balls being dropped from a height under different circumstances. The orange ball is dropped with no horizontal push, so it just falls straight down because of the gravitational force. The blue ball is fired straight out in a setting where there is no gravity acting. Finally, the green ball is sent out with a horizontal push under the action of gravity. It follows the curved path typical of projectile motion.
Projectile motion has two components: a horizontal component caused by the horizontal push, and a vertical component caused by the action of gravity. The horizontal push that the motion starts with is responsible for the horizontal motion. The strength or intensity of the push determines how far the object will travel before landing. The vertical motion is caused by the action of the gravitational force. It determines how long it will take before the object reaches the ground.
Let’s complicate the situation a little. Suppose that our object isn’t sent out horizontally. Instead, it’s sent out at an angle. Then both the horizontal and vertical velocities will depend on the strength or intensity of the initial push, but the vertical motion is still under the influence of the gravitational force. The angle at which the object is projected is very important. The object will travel farthest in the horizontal direction (largest horizontal range) if it is projected at an angle of 45 degrees.
Let’s just think a little more about gravity. Every force in the universe is derived from a combination of four basic forces. Gravitational force is one of these, but the others are the strong (nuclear) force and the weak (nuclear) force, the electromagnetic force as well, of course, as gravitational force. These forces exist naturally, and we don’t really understand what generates them.
What would happen if someone pulled the plug and took gravity away? Life would be very difficult. We’d experience “weightlessness”, and the laws of physics would change. We could no longer assume that what goes up must come down. There would be no reason for anything to “come down”. We would float rather than walk. The gases that make up our atmosphere would no longer be attracted to the Earth, so our atmosphere and the air we breathe would change. In fact, we’d probably suffocate. Physics promise that this will never happen, so we can all breathe a sigh of relief!
Let’s finish the presentation with a brief recap of the concepts we’ve discussed. If you take any pair of objects in the universe that have mass, no matter how far they are apart, they will be attracted to each other with a force we call gravity. The size of this force is directly proportional to the product of the two masses (so it’s bigger for heavier objects) and inversely proportional to the square of the distance between their centres (so it gets smaller as objects get further apart). Gravity gives rise to a form of potential energy (the ability to do work) that depends on how high the objects are above the surface of the planet. Bodies that fall under the action of gravity only are said to exhibit free fall motion. Objects that fall under the action of both a horizontal push and gravity are said to exhibit projectile motion. Finally, no one can turn the gravity off. It is a basic force of nature that will never vanish. And that’s just as well, or we’d be in BIG trouble.