How Do You Calculate Rollercoaster Speeds at Different Points?

[Damie904]

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.

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.

 

[rock.freak667]

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.

 

[PeterO]

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