Calculating Rollercoaster Speed and Spring Constant

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Homework Help Overview

The discussion revolves around two problems related to a rollercoaster's speed at the top of a hill and the spring constant required to launch the rollercoaster. The first problem involves calculating the speed at the top of a second hill after descending from a first hill, while the second problem focuses on determining the spring constant needed to achieve a specific speed after compressing a spring.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of potential energy and kinetic energy in relation to the rollercoaster's motion. Questions arise about how to apply conservation of energy principles and how to incorporate the heights of the hills into their calculations. Some participants consider the effects of mass and velocity on energy transformations.

Discussion Status

Several participants have engaged in exploring the problems, discussing the conservation of energy and how to relate potential energy to kinetic energy. There is a sense of progress as participants clarify their understanding of the concepts involved, although no consensus has been reached on specific calculations.

Contextual Notes

Participants are working under the constraints of providing answers with no units and to two decimal places, which may influence their approach to the calculations. The discussion also reflects a need to consider maximum load limits and minimum speeds in the context of the problems.

fergust
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Hello!

I was hoping somebody could help me with these two problems:

A roller-coaster has a first hill 75.2 meters tall. Immediately after this hill, the roller coaster skims along the ground, then ascends to a second hill 47.8 m tall. If the load limit is 1067.9 kg, how fast is it going at the top of the second hill? As always, no units and 2 decimal places.

The owners of the amusement park have now decided that having a large first hill is too old-fashioned; they now want to use a spring to start the roller coaster. If the starting gate limits the spring to 3.3 meters of compression, and the next hill is now 44.4 meters, what must the spring constant be to lift a load limit of 2280.9 kg to the top with a minimum speed of 18.4? As always, no units and 2 decimal places.


Thank you so much in advance!
 
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Welcome to PF.

How would you think to go about the problems?
 
For the first problem, I know how to find the potential energy at either of the hills, but I'm unsure of how exactly to use this knowledge to find velocity. Or, could I find the velocity at the bottom of the first hill, and then find out how much it decelerates as it climbs the second?
 
fergust said:
For the first problem, I know how to find the potential energy at either of the hills, but I'm unsure of how exactly to use this knowledge to find velocity. Or, could I find the velocity at the bottom of the first hill, and then find out how much it decelerates as it climbs the second?

Isn't there a conservation of energy?

PE becomes KE?

With no friction won't the KE at any point be just the change from the initial PE?
 
LowlyPion said:
Isn't there a conservation of energy?

PE becomes KE?

Yes! So I can find the potential energy at the top of the hill, set that equal to 1/2mv^2, and just solve for v? How do I factor the first hill into that, though?
 
fergust said:
Yes! So I can find the potential energy at the top of the hill, set that equal to 1/2mv^2, and just solve for v? How do I factor the first hill into that, though?

The speed at the top of the second hill is still just the change in PE to that point from the top of the first.

The load limit then is the max mass of the car and riders?
 
The second question is asking you to figure out how much potential energy must be in the spring to propel the car up a 44m hill and still have the KE determined by the max load and the min velocity given.
 
Okay, I think I have them both now. Thank you so much!
 

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