Understanding Conservation of Energy in Rollercoasters

[runicle]

Given the equation Eki + Egi = Ekf + Egi
Which is initial kinetic energy plus initial potential energy equals final kinetic energy plus final potential energy.
If i were to measure the speed of a rollercoaster at the end of its position of a height of 3 and it's initial height is 12 which of these answers are true?
initial / final
1/2*m*vf2 + mgh = 1/2*m*vf2 + mgh
1/2*0 + 9.8m/s2 (12m) = 1/2*vf2 + 9.8m/s2(3)
initial / final
1/2*m*vf2 + mgh = 1/2*m*vf2 + mgh
1/2*0 + 9.8m/s2 (9m) = 1/2*vf2 + 9.8m/s2(0)
*note mass is not included due to they cancel out.

 

[daniel_i_l]

They are both right. It depends on were you take you referance point - at 0 like the first case or at 3 like the second. In both cases you should get the same answer.

 

[Andrew Mason]

Given the equation Eki + Egi = Ekf + Egi
Which is initial kinetic energy plus initial potential energy equals final kinetic energy plus final potential energy.
If i were to measure the speed of a rollercoaster at the end of its position of a height of 3 and it's initial height is 12 which of these answers are true?
initial / final
1/2*m*vf2 + mgh = 1/2*m*vf2 + mgh
1/2*0 + 9.8m/s2 (12m) = 1/2*vf2 + 9.8m/s2(3)
initial / final
1/2*m*vf2 + mgh = 1/2*m*vf2 + mgh
1/2*0 + 9.8m/s2 (9m) = 1/2*vf2 + 9.8m/s2(0)
*note mass is not included due to they cancel out.

You have to tell us what the speed of the rollercoaster is when it is at the top.

Also, your suggested answers do not make sense. The first and third are true by definition. In the second and fourth, what do the (3) and (0) refer to?

AM

 

[daniel_i_l]

I thought that he meant that at the top it was at rest, 0 and 3 are hights

 

[runicle]

what was i trying to find?

 

[daniel_i_l]

the final speed?

 

[runicle]

yes

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Boo yeh!