Main content

## Physics library

### Course: Physics library > Unit 4

Lesson 1: Circular motion and centripetal acceleration- Race cars with constant speed around curve
- Centripetal force and acceleration intuition
- Visual understanding of centripetal acceleration formula
- What is centripetal acceleration?
- Optimal turns at Indianapolis Motor Speedway with JR Hildebrand
- Calculus proof of centripetal acceleration formula
- Loop de loop question
- Loop de loop answer part 1
- Loop de loop answer part 2

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Loop de loop answer part 2

Figuring out the car's average speed while completing the loop de loop. Created by Sal Khan.

## Want to join the conversation?

- What would happen if he went too fast?(50 votes)
- If he went WAAYYY too fast he might break the loop-de-loop. Since the car pushes against the road with the same force that the road pushes against the car.(100 votes)

- Does anybody understand why you would use an "egg shaped"/oval track for this experiment rather than a perfectly circular track?(27 votes)
- There are two main reasons I can detect: One would be the degree of gravitational acceleration; since the acceleration due to gravity is a VERY significant factor a shorter distance (and therefore a shorter time spent with gravity = approx. -9.8m/s^2 Jhat) and greater arc degree is preferable to a longer distance and a smaller arc degree. Two is that the car's ability to maintain a constant speed is inhibited severely by the lack of friction over the top part of the circle/ellipse; so, once again, a shorter distance and greater arc degree is preferable to a longer distance and shorter arc degree. Which gives us a vertically orientated ellipse.(32 votes)

- Since the speed at the top is (approximately) twice the required speed, wouldn't he have normal traction?(8 votes)
- Yes there would be traction(friction); but only in the velocity at the top of the loop is greater than 7.7m/s. This is because you only need 7.7m/s at the top of the loop to stay on, any extra is being counteracted by the normal force (the normal force is adding to the ac rather than just the force of gravity), rather than the weight force. If you ignore friction and propulsion (if he is giving it gas while on the loop) then KEi+ PEi = KEf + PEf. There is no PEi so then we have Initial Kinetic energy is equal to the final (top of loop) kinetic energy and it's Gravitational potential energy. The formula is :

1/2mv^2 = mgh + 1/2mv^2

divide by m since it is in all terms yields

1/2v^2 = gh + 1/2v^2

substitute variables that we know from the video:

1/2(15.3m/s^2) = 9.81m/s^2(12m) + 1/2v^2

117.045 = 117.72 + 1/2v^2

-1(-.675 = 1/2v^2)

1.35 = -v^2

-1.16m/s = v

as you can see the car has to be providing a propulsion force during the loop de loop or else it would have a negative velocity, which would mean falling off of the loop.(7 votes)

- does mass has anything to do about it??(11 votes)
- At1:21in the video, "frames" is used. Does anyone know why it is called "frames" and not kilo-second or something? Thanks.(3 votes)
- This has to do with the way that video is stored on a computer (and how it was originally stored on film).

Back then, video was a series of pictures (or "frames") that were projected one after another on a screen -- very much like a flip-book. In order for the video to not be jumpy like a flip-book can be, they often used 30 frames per second (fps), which gave the impression of real life.

In modern video formats (.mp4, .avi, etc.) there is still this concept of frames, though it gets a bit more complicated because they cut some corners to make the file smaller, such that there might not actually be 30 pictures stored for each second of video.(9 votes)

- What happens when car moves on a plane horizontal circular road... what is the EFFECT OF FRICTION on the horizontal track, if the car starts from rest from a point on the circular track?(2 votes)
- Well, in order to move on a circular road car requires an inward force or force from outside which is ofcourse due to centripital acceleration, but in this case there is no force acting on the car to change its direction so the force required comes from the friction between tires and road if there is no friction, there is no thing which moves it in circular path so in this case the car continue to move in straight line.(6 votes)

- how would you experience an acceleration greater than that of gravity, like when someone says that, for example, you were experiencing 4g's.(4 votes)
- you can search for "g-force training"(1 vote)

- How do you determine the 'margin of safety'? As Mr. Khan said, you can't go too fast, or too slow.(3 votes)
- is 27.6 the speed that the car has to have on the top? if yes then how can we calculate the necessary speed on the bottom?(2 votes)
- Using the speed at the top and other values, such as the mass of the car, etc., you can calculate the potential energy and kinetic energy at the top of the track (giving you the total mechanical energy). Then, using this total energy, you can use the kinetic energy formula to find the speed at the bottom (since there is no potential energy at that point).(3 votes)

- what happens to the car if it goes too fast on the top? could it fall?(1 vote)

## 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 clipped out the parts where he's actually on the loop de loop and I want to figure out his average [speed] 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 we know about the circumference of this loop de loop and we're going to assume that it is perfectly circular for our purpose although it looks like it's a little bit egg-shaped in reality or elliptical For our calculation, we're going to assume that it's perfectly circular I'll leave it to you to think about how it would change if you had an elliptical shape like this So anyway, let's watch the video again Remember this is from fifth gear which shows on Channel 5 in United Kingdom So there you go Let's watch it again. It's fun to watch. There you go And right over here, we have a little timer for my video editor And this right over here is in seconds and I was corrected on a earlier video This right over here is not in hundredth of seconds. This is in frames And there's 30 frames per second So it starts at 0 seconds 0 frames and then when we play it, it goes to 2 seconds and 14 frames There's 30 frames per second So it's 2 and 14/30 of a second. It's how long it takes the car to do the loop So 1 second, and then 2 seconds, 2 and 14/30. So almost 2.5 second So let's write that down So the time required to do the loop de loop is roughly 2 and 14/30 seconds And what is the distance that it travels? If we assume that this thing is circular although it looks like it's a little bit egg-shaped if we assume that it is 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, we figured out the radius was 6 m So it's 2 pi times 6 m which is equal to 12 pi meters If you wanted to figure out its average speed-- the velocity is constantly changing because the direction is changing but the magnitude of the velocity-- if we wanted to figure out the average magnitude of the velocity or the average speed the total distance traveled is 12 pi meters divided by the time required to travel the 12 pi meters so that is 2 and 14/30 seconds Now let's get our calculator out to actual calculate that value So we're going to have the distance 12 pi m divided by 2 + 14/30 just to get the exact value And then this gives us in meters per second 15.3 m/s So the average speed is approximately 15.3 m/s which is almost twice as fast as the minimum speed we figured out 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 force is going to be too big then this--maybe we'll talk about that in the future video I'll just relate this into kilometers per hour. Let's figure out what that is I want to use the calculator here So that's in the meters per second Let's figure out how many meters per hour by multiplying it by 3600 seconds per hour So that's how many meters per hour, and divide it by 1000 which you can see right over there that is 55 km/h If you want to do it in miles, it's rough approximation, divide it by 1.6 It's about 35 mph give or take or 55 km/h So this is approximately 55 km/h So the driver here luckily they did the physics 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 has some nice traction with the track up here