Roller-coaster conservation energy

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SUMMARY

The discussion centers on calculating the initial height required for a roller coaster using conservation of energy principles. The initial potential energy (PEi) was calculated as equal to the final potential energy (PEf) plus kinetic energy (KEf), leading to an initial height of 0.57 meters. After extending the hill by 1.1 meters, the new height becomes 1.67 meters. The percentage increase in height is approximately 300%, indicating a significant adjustment needed for the roller coaster to complete its course.

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Familiarity with potential energy (PE) and kinetic energy (KE) equations
  • Basic algebra skills for manipulating equations
  • Knowledge of percentage calculations
NEXT STEPS
  • Review the principles of conservation of energy in physics
  • Study the equations for potential energy (PE = mgh) and kinetic energy (KE = 1/2 mv²)
  • Learn how to calculate percentage increases and errors in experimental data
  • Explore practical applications of energy conservation in roller coaster design
USEFUL FOR

Physics students, educators, and anyone interested in understanding energy conservation principles in mechanical systems, particularly in the context of roller coaster design and analysis.

Havenater23
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Homework Statement


So I am doing this roller coaster lab in my physics class and I'm having some problems.
You have to find the initial height of a hill and initial velocity; which was easy and I found this out.
PEi = PEf+KEf
m*9.8*h i = m*9.8*0.4572 + 1/2*m*(1.5m/s)^2
m's cancel
assume everything I have put in there is correct. The answer to H(i)=0.57
Even though we got this , our roller coaster using marbles does not complete this. So we had to extend the initial hill ; which is what our teacher wanted us to do. We extended it 1.1 more meters. So now it asked for the percentage to raise the starting point.
Which we did , we used the percent error but we keep getting like 64%
Help would be nice
Thanks


Homework Equations





The Attempt at a Solution

 
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Slightly confusing, I'll give it a shot.

Your initial calculations don't allow for losses so you're going to need more height.

Which you've got, OK.

So far as the "percentage to raise the starting point" goes, surely that would be how much you've increased the starting point height by?

In which case, your initial height is 0.57m. Your new height is 0.57 + 1.1 = 1.67m.

So the percentage increase is nearly 300% - it is nearly 3 times higher than the original starting point.
 

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