If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:4:48

Video transcript

in the last video we figured out the absolute minimum speed in order to stay on the circular path right over here especially near the top was 27.6 km/h what I want to do in this video is I just want to clip I just clipped out the parts where he's actually on the loop-de-loop and I want to actually figure out his average velocity so I'm going to use the video editor right here to time how long it takes to complete the loop-de-loop and then we can use that and what we know about the circumference of this loop the loop and we're going to assume that it is perfectly circular for our assumptions although it looks like it's a little bit egg-shaped in reality or a little bit elliptical but for our calculations we're going to assume that it is perfectly circular and I'll leave you leave it to you to think about how it would change if you had an elliptical shape like this so with that other way let's watch the video again remember this is from fifth gear which shows on the channel five in the United Kingdom so there you go let's watch it again it's just fun to watch there you go and right over here we have the little timer for my video editor and this right over here is in seconds and I was corrected on an earlier video this right over here is not in hundreds of seconds this is in frames and there's 30 frames per second so it starts at zero seconds zero frames and then when we play it it goes to two seconds and 14 frames but that's 30 frames per second so it's two and fourteen thirtieth of a second is how long it takes this car to do the loop so - that's one second and then two seconds - and fourteen thirty it's so almost two-and-a-half seconds so let's write that down so the time and this is all rough because I'm approximating right over here the time required to do the loop-de-loop is two and 14 / thirtieth - over 14 / 30 seconds and what is the distance that it traveled if we assume that this thing is circular although it looks like it's a little bit more egg-shaped if we assume that it's circular then the distance traveled is the circumference of the circular loop-de-loop the circumference is 2 pi times the radius which is equal to 2 pi and in the previous video the previous video we figured out that the radius was 6 meters so it's 2 pi times 6 meters which is equal to which is equal to 12 pi meters so if you want to figure out its average speed I should say the velocity is constantly changing because the direction is changing but the magnitude of the velocity if we want to figure out the average magnitude of the velocity or the average speed we would just have to divide so let me write it over here average speed the total distance traveled is 12 PI meters is 12 PI meters divided by the time required to travel the 12 5 meters so that is 2 + 14 over 32 + 14 over 30 seconds now let's get our calculator out to actually calculate that value so we're going to have the distance is let me clear this so we have 12 PI meters divided by let's write this is 2 plus 14 divided by 30 just to get the exact value to divide plus 14 divided by 30 and then this gives us in meters per second meters per second 15 point I'll just go with 15 point three meters per second so the average speed is approximately fifteen point three fifteen point three meters per second which is almost which is almost twice as fast as we figured out that minimum speed it had to be and that's because you want that margin of safety and you want to be able to have some traction with the road although you don't want to go too fast because then the g-forces are going to be too big then this and maybe we'll talk about that in a future video but just to relate this in two km/h let's figure out what that is woops that's not what I wanted to use I wanted to use this one right over here so that's in meters per second let's figure out how many meters per hour by multiplying by 3,600 seconds per hour so that's how many meters per hour divided by a thousand which you can kind of see right over there that is 55 55 kilometers per hour and if you wanted to do it in miles a rough approximation divided by 1.6 it's about 35 miles per hour give or take or 55 km/h so this is this is approximately 55 km/h so the driver here luckily they did the physics problem ahead of time and he had the margin of safety he was well in excess of the minimum velocity just to maintain the circular motion so he probably had some nice traction with the track up here