in this video I'll cut I will talk about the physics behind the roller-coaster ride so let's say now you're going to design a rollercoaster what should be the minimum speed at the top or at the bottom or on a horizontal level that's the thing I'm going to discuss about in this video and I've chosen one particular numerical to address all the problems so in this particular problem I'll row which is a roller-coaster ride the car and the writer are moving in a vertical droop the radius of the vertical loop is 15 meter that's the radius and we are interested in now the only information given information is the radius which is 15 meter and now what should be the minimum speed at the bottom to make it a complete a vertical loop and what should be if this is the minimum speed where the speed at the top what is the speed at the horizontal level we're going to calculate first thing we're going to start at the top at this top so let's draw the Freebody diagram at the top and here we assuming the roller-coaster is moving along this way they counter clockwise motion ok so the speed at this point or the velocity at this point is tangential which is shown by this arrow they wait at any point is always vertically the downward so this is showing the weight the track is providing a normal force to the writer or to thee the car and the normal force at this point is the downward n stands for the normal force and team is the top so now these two forces ante and MZ together is providing a required centimeter force let me tell you one thing a particle or any object cannot move into a circle without having a force there must be some sort of force which makes them to move into a circle for example the earth is moving around the Sun and the gravitational force of attraction is providing the required centripetal force and in this particular example it is now this normal force and the mg the weight is together providing the required centripetal force and what is the formula or what is the equation for the centripetal force if you recall that's perfectly fine otherwise I'll write it down here MV squared over R is the formula for this centripetal force centripetal force so now let's write down the equation now so at the top the NT the normal force mg is providing the required centripetal force and we're going to solve it for the velocity at the top so what we'll have is NT multiplying our on both sides and dividing by M so this is what we get and we are interested in finding out the minimum speed for the minimum speed the normal force has to be zero so when you plug in the normal force is zero then we get the minimum speed equals to square root of GR and we know the radius is given which is 15 meter and the g value is 9.8 and the speed will get is 12 point 1 2 meter per second about the minimum speed what happens if the rollercoaster does not have this a speed at the top it want to make complete of Article two it will fall down okay so if you are an engineer you should consider all those sorts of things okay so it has to have a minimum of this speed and here was lots of things okay this is an ideal situation ignoring the Air drag denoting the the frictional force lots of things in the ignoring but this but theoretically or ideally this has to be the minimum speed below the speed the car would not able to make a vertical loop now let's do the same thing exactly at the bottom now so again draw a Freebody diagram so the velocity at this point is again tangential and it is along this way if I draw a tangent at this point then that gives you the direction of the velocity and the VP is the magnitude of the velocity which is the speed at that point the weight as always is vertically downward and at this point the track is pushing you upward so so in this case now the required centripetal force is provided by again and be the normal force and mg but the normal force and the weight this time is acting in two opposite direction so any p minus mg provides the centripetal force the negative sign is simply stands for because the weight is in the downward direction so let's write down here so at the bottom and be minus mg is equal to M VA squared over R and then we solve for the the normal force at the bottom this is it now we're going to apply for the conservation of energy again let's come Hokkien it doesn't matter where you are at this point at the top at the bottom isn't a level or at any other point total and nursing is conserved it does not change where you are the total energy has to be exactly the same in this case the total energy includes the kinetic energy kinetic energy and the potential energy GP I am calling this is the gravitational potential energy and this is the kinetic energy and if we add them together these two energy has to be exactly the same at any points so you're going to use the conservation of energy now so applying principle of conservation of energy so this is at the top at the top and this is at the bottom so at the top we have this is at the kinetic energy half MV squared that's the formula for kinetic energy kinetic energy formula is 1/2 M VA squared and the potential or the crab chestnut potential energy is mg H so if we choose this is our reference line for this case then this is the height so the potential energy at the top compared to the bottom is M G and the height is 2 R which is the radius or the diameter in in this case towards the diameter mg 2 R so this is the kinetic energy at the top this is the potential energy at the top and as we have children the bottom is our reference line so this it has only the kinetic energy now in order to have the minimum speed so setting up the VT as a minimum and already have solved the V T minimum is a square root of GR so I'm just plugging this VT into this equation have M the VT R square should be G R which is G our energy - what as it is half M maybe as well now this is the minimum speed that's the minimum speed required because we will have plugged in the VT minimum and the mass cancels out so it doesn't depend upon the mass as you can see here if we solve it what I get is a square root of 5 gr thus the minimum speed required to make a vertical loop and in this particular value if we plug in what I get is twenty seven point one meter per second if it is below twenty seven point one meter per second the car would not be able to make a vertical loop it will fall down and it would be disastrous so now let's again think about the horizontal at this point we are going to use the conservation of energy and as I'm you can choose the reference point at any point so let's choose let's compare the total energy at this point and the total energy at this point the total energy at this point has to be equal to the total energy at this point and I am choosing this as my reference level if I choose this as my reference level then this height will be R and at this point it has the kinetic energy and the potential energy corresponding to this height and it will have only the kinetic energy okay so at the horizontal level this is the kinetic energy now in a technology and potential energy is the CD gravitational potential energy while only our because we have chosen this as my reference level so that after the horizontal level it has only the kinetic energy half MV square and I can and plugging V T when if it is minimum and the formula for VT is a square root of G R so just plug in into this equation so VT square would be equal to G times R MGR half v at square now once you're solve it you'll get V H is equal to 3G our plan all in all values you'll get twenty one meter per second so as you can see the speed are the different point is the different so if you want to make a complete loop from the data then you have to start at twenty seven point one meter per second if if the if it is twenty seven one point one meter per second then it will make a complete vertical loop and it will keep looping around provided there is no friction or there is no other damping all right so this is it for the roller-coaster ride physics problem and again if you have any questions write down your questions in the comment section below and do not forget to Like share and subscribe the channel