Gravity [PHYSICS]

Transcript

hello welcome to attic Academy Matthew here and today I will be be attempting to teach you the basics of gravity at A2 level so to start off with we need a proper definition of what gravity is so essentially gravity is the force of attraction that acts and is experienced by any object with mass so in other words any two objects that have mass will attempt to pull themselves towards one another as I'm sure you experience every day by walking around on the earth so at A2 level you will be required to calculate the force between two objects as opposed to Simply calculating the weight of a singular object on Earth but the question is of course how do you go about doing this well thankfully there's a handy little calculation it's already been created for us which is on the screen now uh now some of you may be a bit confused as to what these symbols actually stand for so I have created a diagram to explain so you've got uh g mm/ r 2 G is the universal gravitational constant it's basically a fixed number there it is now uh you may notice it's actually quite small now the reason for this is because gravity is Believe It or Not the weakest force in the known unit Universe in fact compared to say uh electrostatic force it's quite frankly pathetic and you a lot of people have trouble grasping this because of course we live on a stoning great big ball of rock that sticks Us in place all the time but if you were to hold say a fridge magnet over a paperclip you would notice that of course the magnet attracts a paperclip despite the fact there's an entire planet attempting to pull that paper click down whereas a tiny magnetic field created by something as simple as a fridge magnet is enough to lift up the paperclip um as for the M's big uh Big M and Little M refer to two the two objects in the system now you can name them either way around that you feel like but generally the larger m is dedicated to the larger object because that's logical whereas R is the separation between the center of masses of the two objects sometimes called the radius of the object's orbit so we end up with the gravitational force of attraction is proportional to the product of the two masses and the inversely proportional to the separation squared or the radius squared as it may be this is the actual technical definition that you will be asked to remember in physics exams so I'll just run this through with a simple example of course the Earth and the Moon moon is what Springs to mind instantly so in this example we have to calculate the gravitational force between the Earth and the moon so we have the equation here I've already put out the mass of both the Earth and the moon and the rough uh separation of the center of masses because of course the orbit of the moon Alters but that's not important at the moment so first of we put in the Universal gravitational constant uh followed by the two masses of the object followed by the separation squared and that will give you the answer of 1.98 * 10 ^ 20 newtons so all quite simple I'm sure you will agree moving on to gravitational fields now you will be uh required to remember stuff just general things about gravitational field for the exam and one of these things is how to draw them now there are two main ways of drawing gravitational fields which I'm going to cover here first of all you have equip potentials now equip potentials are lines that represent an increase by a set of mounting the field so in this example I've said 10 Newtons uh so we have the point Mass here so at say this line the force may be 10 Newtons at this one 20 at this one 30 and so on and so forth you will notice that these lines spread out as you move away from the um object in question this is because of course the radius is squared so as you increase the rate of the rate at which the um Force decreases also increases so in other words as you move out the size of the force get smaller quicker the other way is using field lines now these are lines that show the magnitude and direction of the force the majority of the time you'll be working with a sphere so the arrows will will be of the same size anyway and we can all Point towards the center this is basically the default way of drawing the field uh if you're asked to draw a field and it doesn't specify this will be the one that you end up drawing now field strength you'll also be required to calculate the strength of the field at a specific point so uh field strength is measured is a measure of how much force an object would experience per kilogram if it was place in a specific point in the field and uh it can be calculated by using the equation gm/ R 2 because what you're essentially doing is removing the Little M from the previous uh equation and replacing it with one so yeah I've just written that there finally the last thing you'll be asked to do with gravity is to calculate gravitational potential now this is where things get a little bit confusing because in order to measure the potential we need to have a reference point to measure it from where the potential is zero however gravit gravity is an infinitely reaching force it will continue to decrease the further you go from an object and the smaller the object gets but it will never actually really reach zero the only point that will ever occur is at Infinity because then um R will equal infinity and then anything over INF must equal uh zero so we have to use Infinity as a reference point so that's that's all well and good so we now have a reference point to to measure from which gives us the following definition the gravitational potential at a point in a field is a work done per unit Mass to move an object from Infinity to that point in other words it's the work you need to do to push an object into that point in the field from Infinity so and uh potential is equal to force time distance now we already have an equation for force that was uh GM m/ R so GMM / r^ s multip r we end up simplifying it down to gm/ R because Little M is equal to one again because as I mentioned this is per the amount of work we have to do per unit mass in other words per kilogram to move something in so we just use gm/ R now there is a bit of a problem though because GM over R is not correct as I will hopefully explain with this diagram so we now have a uh system if you like where Infinity is zero and everything refers back to Infinity so we have the positive running from the object towards Infinity so that direction is positive so that direction is positive unfortunately if we were to place the object in the field it would be attracted to the other object in other words the force would be acting in a negative Direction therefore the object at that point in the field must have a negative potential because it intends to go in the same way as the force so the calculation for Infinity must therefore be netive gm/ R CU also if you think about it um the potential energy is work done to move an object from Infinity to to a point in a field we do not actually have to do work on that object it will instinctively want to go towards the other object so it will always be a negative value so I thought I'd best explain this with example back to the Earth and Moon example so simply plug in the values so we have the mass so we want to find the potential the potential of the Moon in its orbit around the Earth so we simply placing the mass of the Earth multiplied by the grav by the universal gravitational constant over the radius of the moon's orbit and we then end up with this value so we now have a value for the gravitational potential per kilogram of an object that's in the orbit radius of the Moon but we want to find the total potential of the Moon itself so in order to do that we need to multiply this per kilogram unit by the actual mass of the Moon like so and that will give us the total potential energy of the Moon which is 7.62 * 10 ^ 22 jewles so in other words it's qu got quite a lot of potential and well that's pretty much it really thank you for watching um if there is anything else you would like us to co cover please leave a comment below and I hope to see you next time