Help with an energy problem found on the Phet Website

  • Thread starter Rainy_Pass
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In summary, the question asks for the maximum height the coaster can go over the second hill, but does not provide information about the amount of energy needed.
  • #1
Rainy_Pass
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Homework Statement



A 1000 kg roller coaster begins on a 10 m tall hill with an initial velocity of 6m/s and travels down before traveling up a second hill. As the coaster moves from its initial height to its lowest position, 1700J of energy is transformed to thermal energy by friction. In order for the roller coaster to safely travel over the second hill, it must be moving at a velocity of 4.6m/s or less at the top of the second hill. What is the maximum height the second hill can be?

Homework Equations



KE = .5mv2
GPE = mgh
total energy = PE + KE + The

The Attempt at a Solution



PEmax = Total energy
PE = 1000kg (9.8 m/s2) 10m = 98,000J
KE = .5 (1000 kg) 4.62 = 10,580 J

Energy left at the bottom of the roller coaster = 98,000J - 1,700 J = 96,300 J

96, 300 J - 10,580 J = 85,720J

85,720 J = 1000kg (9.8 m/s2) h

h = 8.75m
 
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  • #2
The question is a bit strange, and I'm not sure whether it is a mistake or it is deliberately laying a trap.
It provides a maximum speed for going over the second hill, but asks for a maximum height. Do you not see something odd about that?
 
  • #3
The explanation looks reasonable, but it's not the correct answer according to the answer key. The answer key says that it's 7.3 m, but gives no explanation of how to get the answer.
 
  • #4
mfig said:
Need to use:

85720-1000(4.6)(4.6)/2=1000(9.8)h
The first answer already subtracted the KE at the top of the second hill to get to 85720J, so why would you subtract it a second time? I'm trying to figure out the discrepancy between what the answer key is giving for a correct answer (7.3m) and what Rainy_Pass got for an answer (8.5m). The only thing that I can figure out is that the amount of thermal energy needs to be accounted for as a percentage, not a fixed amount. My Math skills aren't good enough to figure out how to put that into the equations though.
 
  • #5
jackie311 said:
The first answer already subtracted the KE at the top of the second hill to get to 85720J, so why would you subtract it a second time? I'm trying to figure out the discrepancy between what the answer key is giving for a correct answer (7.3m) and what Rainy_Pass got for an answer (8.5m). The only thing that I can figure out is that the amount of thermal energy needs to be accounted for as a percentage, not a fixed amount. My Math skills aren't good enough to figure out how to put that into the equations though.
The OP forgot the initial 6m/s. This may have confused @mfig .
As I posted, the question is strange. The maximum velocity at the end imposes a minimum height on the second hill. To find the maximum height we don’t need that. I suspect the full question asked, or was intended to ask, the min and max heights.

Another puzzle is whether we are supposed to consider friction in the ascent. Why would it suddenly cease? Ignoring that, I get heights over 10m for both min and max, so it looks like friction should be considered to continue, but we don’t know how to allow for it. Proportional to height, perhaps.
 

Related to Help with an energy problem found on the Phet Website

1. What is the Phet website?

The Phet website is a free online platform developed by the University of Colorado Boulder that offers interactive simulations for teaching and learning science, math, and engineering. It is used by millions of students and teachers around the world.

2. How can the Phet website help with an energy problem?

The Phet website offers a wide range of simulations related to energy, such as energy skate park, energy forms and changes, and energy skate park: basics. These simulations allow users to manipulate variables and observe how energy behaves in different scenarios, helping them understand and solve energy problems.

3. Are the simulations on the Phet website accurate?

Yes, the simulations on the Phet website are based on scientific research and are rigorously tested and verified by experts. They are constantly updated to ensure accuracy and reflect the latest scientific knowledge.

4. Can I use the Phet simulations for commercial purposes?

No, the Phet website and its simulations are free for non-commercial use only. If you wish to use them for commercial purposes, you must obtain permission from the University of Colorado Boulder and properly credit the source.

5. Are there any age restrictions for using the Phet simulations?

No, the Phet simulations are designed for a wide range of ages and can be used by anyone with basic computer skills. However, some simulations may require a certain level of understanding of the underlying concepts, so it is recommended to choose simulations appropriate for the user's age and knowledge level.

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