Find the ration of the centripetal accelaration

AI Thread Summary
The discussion revolves around calculating the ratio of centripetal acceleration at the tip of a helicopter blade (6.7m) to that at a point 3.0m from the center. The formula for centripetal acceleration, Ac = V^2/r, is emphasized, with the need to express speed (v) in terms of radius (r) and period (T). Participants struggle with understanding the concepts of revolution and period, which are crucial for solving the problem. The correct answer for the ratio of centripetal accelerations is determined to be 2.2, highlighting the importance of grasping the underlying physics principles. Overall, the conversation stresses the necessity of foundational knowledge in circular motion to solve such problems effectively.
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The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 6.7m, measured from its tip to the center of the circle. find the ration of the centripetal accelaration at the end of the blade to that which exists at a point located 3.0m from the center of the circle?

the answer is 2.2

i don't know to get 2.2
 
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Show us what you have attempted so far. Start with the formula for centripetal acceleration.
 
Cyosis said:
Show us what you have attempted so far. Start with the formula for centripetal acceleration.

centripetal acceleration
Ac = V^2/r
 
Yes and you know that the blade describes a circle. So how can you calculate v in terms of the radius and period?
 
Cyosis said:
Yes and you know that the blade describes a circle. So how can you calculate v in terms of the radius and period?

Ac = 6.7m^2/3m
= 44.89m/3m
= 14.96

the answer is 2.2 not 14.96
 
The length of the blade is 6.7m, how can that be equal to its speed? Length and speed are not the same! I will ask again how can you express v in terms of the radius and period?
 
Cyosis said:
The length of the blade is 6.7m, how can that be equal to its speed? Length and speed are not the same! I will ask again how can you express v in terms of the radius and period?

i didn't understand it
 
What part do you not understand and why are you ignoring my question for the second time? If you are unwilling to cooperate we're not going to get anywhere. I will guide you to the answer, but only if you cooperate.
 
Cyosis said:
What part do you not understand and why are you ignoring my question for the second time? If you are unwilling to cooperate we're not going to get anywhere. I will guide you to the answer, but only if you cooperate.

60 degrees
 
  • #10
'the circle of degrees is 60' makes no sense to me. It is also irrelevant to the problem. For the third time now I will ask you the following question:

How can you express the speed v, in terms of the radius r, and the time it takes for one revolution T?
 
  • #11
Cyosis said:
'the circle of degrees is 60' makes no sense to me. It is also irrelevant to the problem. For the third time now I will ask you the following question:

How can you express the speed v, in terms of the radius r, and the time it takes for one revolution T?

what is T revolution
 
  • #12
As I said, the time it takes for one revolution, the period.
 
  • #13
Cyosis said:
As I said, the time it takes for one revolution, the period.

how?
 
  • #14
Could you be a little bit more specific when it comes to asking questions and giving answers. Single phrase 'sentences' really don't work well to convey a message. I do not see how the sentence you quoted from me can generate the question 'how'? How what?
 
  • #15
Cyosis said:
Could you be a little bit more specific when it comes to asking questions and giving answers. Single phrase 'sentences' really don't work well to convey a message. I do not see how the sentence you quoted from me can generate the question 'how'? How what?

the time it takes for one revolution, the period.
 
  • #16
We are having serious communication issues here. Do you know what a revolution is, do you know what a period is? If you do, explain both concepts to me.
 
  • #17
Cyosis said:
We are having serious communication issues here. Do you know what a revolution is, do you know what a period is? If you do, explain both concepts to me.

i don't know what is revolution and period
 
  • #18
The blade describes a circle, it rotates. After some time T the blade returns to its original position at that point in time it has done one full rotation called a revolution. The time it takes for the blade to make one circle is called the period. You want to know the speed of the blade at a distance r from the center.
 
  • #19
Cyosis said:
The blade describes a circle, it rotates. After some time T the blade returns to its original position at that point in time it has done one full rotation called a revolution. The time it takes for the blade to make one circle is called the period. You want to know the speed of the blade at a distance r from the center.

R is 3 m
 
  • #20
R can be all values in between 6.7 and 0. You have a formula for the centripetal acceleration with two variables r and v. r is known but v is not therefore we want to find v. I have been telling you to do this for the fourth time now.

If you pick a certain point on the propeller blade and let the blade rotate until it comes back to its original position. How much distance has that point traveled? hint: the blade describes a circle
 
  • #21
Cyosis said:
R can be all values in between 6.7 and 0. You have a formula for the centripetal acceleration with two variables r and v. r is known but v is not therefore we want to find v. I have been telling you to do this for the fourth time now.

If you pick a certain point on the propeller blade and let the blade rotate until it comes back to its original position. How much distance has that point traveled? hint: the blade describes a circle

6.7m
 
  • #22
Great another one phrase answer without any explanation to why you think that is the answer. Are you just guessing or what? The blade is 6.7m LONG and is rotating. I placed a point a distance r from the enter on the blade, never did I say the point was on the tip of the blade.

The blade is rotating it describes a circle do you see this? (answer this question)
Therefore the point on the blade follows the circumference of that circle. How much distance does the point move during one revolution? (answer this question)
 
  • #23
Cyosis said:
Great another one phrase answer without any explanation to why you think that is the answer. Are you just guessing or what? The blade is 6.7m LONG and is rotating. I placed a point a distance r from the enter on the blade, never did I say the point was on the tip of the blade.

The blade is rotating it describes a circle do you see this? (answer this question)
Therefore the point on the blade follows the circumference of that circle. How much distance does the point move during one revolution? (answer this question)

i dunno
 
  • #24
So you don't know a single one of those questions? I must say you don't make me feel like you are actually trying to understand this. So I am going to try one more time.

Do you understand and see how the blade describes the circumference of a circle when it starts rotating?
What is the circumference of that circle?

Answer both questions separately.
 
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  • #25
Cyosis said:
So you don't know a single of those questions? I must say you don't make me feel like you are actually trying to understand this. So I am going to try one more time.

Do you understand and see how the blade describes the circumference of a circle when it starts rotating?

the length is 6.7 m and the center of the circle is 3
 
  • #26
i need to solve now
 
  • #27
No that's wrong, besides that's not even what I asked. The center of the circle is at a distance 0, the 3m value is almost half way on the blade and the 6.7m value is at the tip of the blade. Read post #24 again and answer my questions.
 
  • #28
Cyosis said:
No that's wrong, besides that's not even what I asked. The center of the circle is at a distance 0, the 3m value is almost half way on the blade and the 6.7m value is at the tip of the blade. Read post #24 again and answer my questions.
i did not understand how the blade describes the circumference of a circle when it starts rotating?
What is the circumference of that circle?

3.1416 is pi r

c=2(3.1416)r
 
  • #29
That makes no sense. What you wrote there is 3.1416=\pi r. Presumably this is the answer to the question what the circumference of the circle is? Well obviously this answer is wrong. Try again, what is the formula of the circumference of any circle?
 
  • #30
Cyosis said:
That makes no sense. What you wrote there is 3.1416=\pi r. Presumably this is the answer to the question what the circumference of the circle is? Well obviously this answer is wrong. Try again, what is the formula of the circumference of any circle?

c = 2 pi r
 
  • #31
Yes so the distance the point on the blade travels is?
 
  • #32
cyosis said:
yes so the distance the point on the blade travels is?

18.8496
 
  • #33
What did I say about randomly writing down a number or not. The point is at a distance r, I don't see how we can get a numerical value. So if the point is at a distance r from the center the circumference of the circle it describe is? Don't just show your answer also show your calculation.

Now remember that one revolution takes time T to complete. You now know the distance the point traveled and how long it took. So the speed of the point around the circle is?

Does a point on the tip of the propeller has the same period as a point on the center of the blade?
 
  • #34
cyosis said:
what did i say about randomly writing down a number or not. The point is at a distance r, i don't see how we can get a numerical value. So if the point is at a distance r from the center the circumference of the circle it describe is? Don't just show your answer also show your calculation.

Now remember that one revolution takes time t to complete. You now know the distance the point traveled and how long it took. So the speed of the point around the circle is?

Does a point on the tip of the propeller has the same period as a point on the center of the blade?

c = 2 (3.1416)(3)
c = 18.85
 
  • #35
jandominic145 - I suggest that you start being more helpful to those who are trying to assist you in your studies. Most people here are extremely patient and happy to help those people who are willing to put some effort into their studies. However, you must realize that everyone's time is finite and unless you start making more of an effort and actually try to solve the problems yourself without having the solution handed to you on a platter then you will quickly find yourself without any help at all.

Now, Cyosis has been more than helpful and has virtually given you the algorithm required to solve the problem several times. I suggest that you take a breath and then look at Cyosis' posts and see if you can solve the problem without asking any additional questions.
 
  • #36
ok Hootenanny
 
  • #37
This problem may be more easily solved this way.

The blade tip is rotating. It rotates with a time period (T). You can define the angular velocity (w) for any object moving in a circle. If the object makes one full rotation as it does in this case then;

w = 2*pi/T (eq.1)

Remember that the angle made by a complete rotation in a circle full is 2 pi radians.
Angular velocity has units of s^-1. Sometimes you will see the units quoted as rads/s these are the same thing as radians are dimensionless. Also not that the angular velocity is the same no mater what the radius of rotation is. It is only dependent on the period of rotation.

Now you can relate the angular velocity to the tangential speed (v) of the rotor tip. This is the speed that the tip would move in in a straight line if it brake away from the rest of the blade.

v = w*r (eq.2) units m/s

You gave earlier the formula for centripetal acceleration (a) as;
a =V^2/r

Now substitute eq.2 into eq.3.

<< solution deleted by berkeman >>

I hope this helps. While Cynosis has spent a lot of time trying to help you I do feel Cynosis that you assumed more knowledge and understanding than jandominic145 has on this subject, which is why he posted. By the way word answers usually signify confusion and lack of understanding rather than laziness. Confusion can also lead to the rabbit in the headlight situation with no idea what to ask or how to ask it.
 
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  • #38
I actually assumed very little knowledge. All I assumed is that he knew the circumference of a circle, x=vt and the formula for centripetal acceleration. What you just did is spoon feed him the entire solution while adding some more formulas that he may or may not know but certainly won't understand. He will certainly be able to find the answer right away now, but will he understand why?
 
  • #39
He did not understand before at all. So he could go away and read up or read that. Either way he needs to read up. If he was in his class his teacher would probably have to break the problem down for him to solve it anyway. That what I did. If he does not understand he can come back with specific questions now rather than I dunno. Put is this way if you are a student at school and you are stuck and all you get of your teacher are little snippets of information that you do not understand you remain stuck (and probably give up), unless someone breaks the problem down into manageable chunks. After a few problems like this he will get the idea of how to solve further problems without such help.

I am not belittling you efforts at all, you spent a fair bit of time trying to help him but he was still none the wiser against your efforts which indicates a lack of understanding that needed to be plugged. So a different approach to the problem is needed.

Also if they are studying circular motion it is a fair bet that they have already covered the angular velocity at least that what our curriculum does.
 
  • #40
bm0p700f said:
He did not understand before at all. So he could go away and read up or read that. Either way he needs to read up. If he was in his class his teacher would probably have to break the problem down for him to solve it anyway. That what I did. If he does not understand he can come back with specific questions now rather than I dunno. Put is this way if you are a student at school and you are stuck and all you get of your teacher are little snippets of information that you do not understand you remain stuck (and probably give up), unless someone breaks the problem down into manageable chunks. After a few problems like this he will get the idea of how to solve further problems without such help.

I am not belittling you efforts at all, you spent a fair bit of time trying to help him but he was still none the wiser against your efforts which indicates a lack of understanding that needed to be plugged. So a different approach to the problem is needed.

Also if they are studying circular motion it is a fair bet that they have already covered the angular velocity at least that what our curriculum does.

I understand your frustration, bm0p700f, but we still do not give out detailed solutions here. It does not help the student to learn how to learn. I edited your post to try to leave the tutorial hints, but get rid of the details on how to get the answer to the problem.

Cyosis -- you have an amazing patience. Thank you for your efforts.
 
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