Calculating Maximum Speed and Acceleration for an Amusement Park Ride

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Homework Help Overview

The discussion revolves around calculating maximum speed and acceleration for an amusement park ride that operates in a horizontal circular motion with a specified radius. The problem involves understanding centripetal acceleration and its limits for safety, as well as the implications of changing tangential speed.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants attempt to calculate maximum tangential speed based on given centripetal acceleration limits and question the correctness of their calculations.
  • Some participants express uncertainty regarding the treatment of acceleration as a vector in different contexts, particularly when comparing the amusement park ride to a bike traveling in a circular path.
  • There are discussions about the implications of increasing speed on acceleration and the need to consider both radial and tangential components of acceleration.

Discussion Status

The conversation includes various attempts at calculations, with some participants questioning their results and others providing insights into the vector nature of acceleration. There is an ongoing exploration of how to approach related problems, particularly regarding the distinction between constant speed and changing speed in circular motion.

Contextual Notes

Participants note the importance of using gravitational acceleration in calculations and the potential confusion arising from different problem setups. There is also mention of homework constraints and the need to adhere to specific guidelines in problem-solving.

veronicak5678
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Homework Statement



An amusement park ride carries riders in a horizontal circle with radius 5m.

1) If the centripetal acc. is limited to .4 g for safety, what is the max tangential speed?
2) If the tangential speed is doubled, what is the new acceleration?

Homework Equations



A= v^2/r


The Attempt at a Solution



1) (.4g(5m))^(1/2)
max speed = 1.41 m/s

2) A = 2root2 m/s / 5m = 1.6 m/s^2

Does this look right?
 
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veronicak5678 said:

Homework Statement



An amusement park ride carries riders in a horizontal circle with radius 5m.

1) If the centripetal acc. is limited to .4 g for safety, what is the max tangential speed?
2) If the tangential speed is doubled, what is the new acceleration?

Homework Equations



A= v^2/r

The Attempt at a Solution



1) (.4g(5m))^(1/2)
max speed = 1.41 m/s

2) A = 2root2 m/s / 5m = 1.6 m/s^2

Does this look right?

Yep.
 
OK!
I wasn't sure because the next problem refers to a bike traveling around a circular curve and asks for acceleration. I was going to do the same thing, but there's a note next to the question that says "Remember this is a vector!". Why is that a vector and not this?
 
veronicak5678 said:

Homework Statement



An amusement park ride carries riders in a horizontal circle with radius 5m.

1) If the centripetal acc. is limited to .4 g for safety, what is the max tangential speed?
2) If the tangential speed is doubled, what is the new acceleration?

Homework Equations



A= v^2/r


The Attempt at a Solution



1) (.4g(5m))^(1/2)
max speed = 1.41 m/s

I don't believe this is correct; I think you forgot to multiply by the factor of g.

2) A = 2root2 m/s / 5m = 1.6 m/s^2

Does this look right?

The acceleration started out as (0.4 g) which is about 4m/s^2, and increasing the speed will not make the acceleration decrease.
 
I see. Using 9.8 m/s^2 for g, I get 19.6^(1/2) m/s for part 1 and 15.68 m/s^2 for part 2.
Still don't understand the next question. How can I calculate acceleration on a curve as a vector?
 
veronicak5678 said:
I see. Using 9.8 m/s^2 for g, I get 19.6^(1/2) m/s for part 1 and 15.68 m/s^2 for part 2.
Still don't understand the next question. How can I calculate acceleration on a curve as a vector?

He's right. I missed the g. Sorry.

As to the acceleration that's given by v2/r but it's radially directed. If the tangential speed is also accelerating then the value of the tangential acceleration is a vector that is added to the radially directed centripetal acceleration.The resultant vector is then directed at an angle to the radius.

Btw: the first one is a vector too. It's radial. The question though was only concerned with its magnitude.
 
Last edited:
Um, not sure I get all that.
This problem deals with constant speed, so I assume the tangential speed is not increasing.

It says " A bike travels around a circular curve of radius 80m at a constant speed of 10 m/s.
1) Calculate the bike's acceleration.
2) The bike slows uniformly to rewst in 6 seconds. Calculate the tangential acceleration component.
3) The instant the bike is traveling 8 m/s, determine total acceleration.
 
veronicak5678 said:
Um, not sure I get all that.
This problem deals with constant speed, so I assume the tangential speed is not increasing.

It says " A bike travels around a circular curve of radius 80m at a constant speed of 10 m/s.
1) Calculate the bike's acceleration.
2) The bike slows uniformly to rest in 6 seconds. Calculate the tangential acceleration component.
3) The instant the bike is traveling 8 m/s, determine total acceleration.

In the first part, you calculate the the V2/r as before.

In the second part the tangential is slowing so there is also a (-) tangential acceleration. This is a vector too.

The third part is asking you when the V is 8, and it's slowing at the negative tangential rate, what is the sum of those 2 vectors. Since the tangential is negative it will be trailing the radial vector at an angle.
 
Last edited:
OK, I think I get it. I'm going to go take a break before I try this. Thanks a lot for helping!
 

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