How Do You Calculate Rollercoaster Speeds at Different Points?

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SUMMARY

The discussion focuses on calculating rollercoaster speeds at various points using the conservation of energy principle. The initial height (h1 = 50 m) allows for the calculation of speed at point 2 (v2 = 31.304 m/s) using the formula v = √(2 * g * h). For points 3 and 4, the change in potential energy must be considered, specifically using the heights h1 - h3 and h1 - h2 respectively to determine the speeds. The correct application of energy conservation is essential for accurate calculations at all points.

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  • Understanding of gravitational potential energy and kinetic energy concepts
  • Familiarity with the conservation of energy principle
  • Proficiency in using the formula v = √(2 * g * h)
  • Basic knowledge of rollercoaster dynamics and physics
NEXT STEPS
  • Study the conservation of mechanical energy in physics
  • Learn how to apply energy conservation to different mechanical systems
  • Explore advanced applications of potential and kinetic energy in rollercoaster design
  • Investigate the effects of friction and air resistance on rollercoaster speeds
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Damie904
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Homework Statement


The roller-coaster car shown in Fig. 6-41 (h1 = 50 m, h2 = 13 m, h3 = 25 m), is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4.
6-41alt.gif



Homework Equations


v2= Square Root of 2*Gravity*Height


The Attempt at a Solution


I used the formula to figure out the speed at point 2( which was 31.304 m/s) but it doesn't seem like the same formula works for points 3 and 4 so I'm guessing I need another formula to figure out the other 2 points, although I have no clue what that might be.
 
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From 1 to 2, the cart is released from rest at maximum height h1.

So the total energy is the PE at point 1.

If you want the energy conversion between 1 and 3 then you need to see that the PE at point 3 would include the change in PE from 1 to 3 and the KE at 3.

Use conservation of energy to get this speed.
 
Damie904 said:

Homework Equations


v2= Square Root of 2*Gravity*Height


mis-leading equation here. the reference to height should say "change of height"

For Point 2, the change of height is h₁

For point 3, the change of height is (h₁ - h₃)

For Point 4, the change of height is (h₁ - h₂)Peter
 

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