Rollercoaster velocity question, only given: radius of loop.

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Homework Help Overview

The problem involves a rollercoaster moving through a loop with a radius of 20m. The original poster seeks to determine the speeds at various positions along the track and the height difference between two points, given specific conditions about friction and energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the conservation of energy principle but expresses uncertainty about how to proceed without knowing mass or height. Some participants suggest using energy conservation between different positions and question the types of energy involved at those points.

Discussion Status

Participants are exploring the application of conservation of energy to solve for velocities at different positions. There is an acknowledgment of a typo regarding friction, and some guidance has been offered about the relationship between energy at different points. The original poster later reports having found values for the velocities and height difference, indicating some progress in the discussion.

Contextual Notes

The discussion includes a note about the assumption of negligible friction and the need to consider energy types at various positions. There is also a mention of a specific formula used for calculating velocity at one position.

MelissaJL
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Homework Statement


A7Q1.png

The rollercoaster moves freely without negligible friction. The radius of the loop is 20m and the car barely makes it through the loop.
Find the speed at position 3.
Find the speed at position 1 and 2.
Find the difference in height between position 1 and 4 if the speed at position 4 is 10m/s.

The only part I've been able to solve so far is position 3 which I used the formula:
v=√gR=√196=14m/s

I'm not sure what direction to take for position one and two and was wondering if I could get help with those two parts. Thank you so much :)
 
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MelissaJL said:
... moves freely without negligible friction...

I think that you mean 'with negligible friction'.

For position 1 and 2 you can try using conservation of energy.
 
Oh yes. That is a typo, it moves with negligible friction. I understand that this is a conservation of energy but I am lost on how to use the formula without knowing the mass or height to then solve for velocity.
 
re speed at position 1:

Energy at 3 = energy at 1

What kind of energy at 3?
What kind of energy at 1?

Note that the height at 3 = 2 x radius and you do not need the mass because it eliminates itself.
 
Thanks I figured it out. The values are for point 1 the velocity is 31.3 m/s. For point 2 the velocity is 24.2m/s. Lastly, the height differences between 1 and 4 is 44.9m. That was great help. :)
 

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