Centripetal acceleration
Loop De Loop Answer part 1 Figuring out the minimum speed at the top of the loop de loop to stay on the track
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- What I want to do now is figure out what's the minimum speed
- that the car has to be at the top of this loop de loop in order to
- stay on the track, in order stay in a circular motion, in order to not fall down like this
- I think we can all appreciate that that is the most difficult part of the loop de loop
- At least at the bottom half right over here
- the track itself is actually providing the centripetal force to keep it going in a circle
- But when you get to the top
- you now have gravity that is pulling down on the car almost completely
- and the car will have to maintain some minimum speed in order to stay in its circular path
- Let's figure out what that minimum speed is
- To help figure that out, we have to figure out what the radius of this loop de loop is
- Actually it's not a perfect circle based on this little screen shot that I got here
- it looks a little bit elliptical
- but it looks like the radius of curvature right over here is actually
- smaller than the radius of the curvature of the entire loop de loop
- So if you made this into a circle, it would actually be even a smaller circle
- But let's just assume for the sake of our argument right over here
- this thing is a perfect circle, and if it was a perfect circle, let's think about
- what that minimum velocity would have to be up here at the top of the loop de loop
- So we know that the magnitude of your centripetal acceleration is going to be equal to
- your speed squared divided by the radius of the circle that you are going around
- Now at this point right over here at the top, which is going to be the hardest point
- the magnitude of our acceleration, this is going to be 9.81 meters per second squared
- And the radius we can estimate. I copied and pasted the car and it looks like
- I can get it to stack on itself 4 times to get the radius of this circle right over here
- I looked it up on the web and a car size is going to be about 1.5 m high
- from the bottom of the tires to the top of the car
- And so it looks like just eyeballing it based on these copying and pasting of the cars
- the radius of this loop de loop here is 6 m
- So this right over here is 6 m
- Actually we could just in the variables
- just to manipulate so we can solve v
- We have v squared over r is equal to a
- and then you multiply both sides by r, you get v squared is equal to a times r
- And you take the principal square root of both sides
- You get v = the principal square root of a times r
- And then if we plug in these numbers
- this velocity that we have to have in order to stay in the circle
- is going to be the square root of 9.81 m/s squared times 6 m
- and you can verify that. These units work out. Meters times meters is meter squared
- per second squared
- You take the sqrt of that. You get meters per second
- Let's get our calculator out to actually calculate this
- So we are going to get the principal square root of 9.81 times 6 m
- It gives us--and here's our drumroll
- 7.67. I'll just round it three significant digits, 7.67 meters per second
- Significant digits in our conversation
- This is just a very very rough approximation, I am unable to measure this accurately at all
- but I get a roughly 7.67 meters per second. Approximately 7.7 m/s
- And just to give you a sense of how that translates into units that we're used to
- when we're driving cars
- I'll take 7.7 m/s. If you want to say how many meters you go in an hour
- well, there's 3600 seconds in an hour
- and if you want to convert that into kilometers
- this will be in meters, you divide by 1000. 1 km is equal to 1000 m
- These units will cancel out. You have meters, meters; seconds, seconds
- You're left with km/h
- Let's actually calculate this
- And so we get our previous answer and we want
- multiply it times 3600 to figure out how many meters in an hour
- and then you divide by 1000 to convert to kilometers per hour
- So you divide by a thousand
- And we get 27.6 km / h
- which is surprisingly slow. I would've thought that it would be much much much faster
- but it turns out it doesn't have to be much much faster. Only 27.6 km/h
- Now the important thing to keep in mind is
- this is just fast enough at this point to maintain the circular motion
- But if this were a perfect circle right over here, and you're going in exactly 27.6 km/h
- you would not have much traction with the road. If so
- the car might slip and might not be able to actually maintain its speed
- So you definitely want your speed to be a good bit larger than this
- in order to keep a nice margin of safety
- in order to especially have traction with the actual loop de loop to maintain your speed
- What I want to do in the next video is actually time the car
- to figure out how long it takes to do this loop de loop
- We're gonna assume that it's a circle
- and we're gonna figure out how fast its actual average velocity was
- over the course of this loop de loop
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
|
Have something that's not a question about this content? |
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.