I am a little confused about kinetic and potential energy regarding roller coasters. I understand that the first hill has to be the highest to gain the potential energy (PE).

I hope someone can help with this example I just made up to help me understand:

1st Hill: 50 m from ground
1st Drop: 10 m from ground
2nd Hill: 40 m from ground
2nd Drop: 1 m from ground
3rd Hill: 45 m from ground

Are my explanations correct:
1st Hill: gains the maximum potential energy (PE) and zero kinetic energy (KE)?
1st Drop: gains KE, but still has some PE since its not to 0 meters from ground?
2nd Hill: mostly PE, and a little KE?
2nd Drop: mostly, mostly KE, a little tiny PE?
3rd Hill: mostly PE, a tiny bit KE?

-Does it matter that the 3rd hill is bigger than the 2nd hill? Is it the 1st hill that matters?

-If there is a drop lower than the first drop (like 2nd Drop and 1st Drop above), will all the PE from the 1st Hill still go to ALL kinetic energy in the 1st drop even though its not all the way to the bottom/isn’t the lowest drop?

1st Hill: 50 m from ground

1st Drop: 10 m from ground
2nd Hill: 40 m from ground
2nd Drop: 1 m from ground
3rd Hill: 45 m from ground

Are my explanations correct:
1st Hill: gains the maximum potential energy (PE) and zero kinetic energy (KE)?

AGREE (ASSUMING IT IS STOPPED UP THERE)

1st Drop: gains KE, but still has some PE since its not to 0 meters from ground?

AGREE

2nd Hill: mostly PE, and a little KE?

AGREE

2nd Drop: mostly, mostly KE, a little tiny PE?

AGREE

3rd Hill: mostly PE, a tiny bit KE?

AGREE

-Does it matter that the 3rd hill is bigger than the 2nd hill? Is it the 1st hill that matters?

YES, EXACTLY, MAXIMUM HEIGHT DETERMINES TOTAL ENERGY AVAILABLE

-If there is a drop lower than the first drop (like 2nd Drop and 1st Drop above), will all the PE from the 1st Hill still go to ALL kinetic energy in the 1st drop even though its not all the way to the bottom/isn’t the lowest drop?

NO, THE PE DOES NOT GO TO ZERO UNTIL THE CAR IS AT GROUND LEVEL.
YOU ALREADY ANSWERED THAT IN YOUR ANSWER TO THE FIRST QUESTION:
1st Drop: gains KE, but still has some PE since its not to 0 meters from ground?

BY THE WAY, THE SELECTION OF ZERO POTENTIAL ENERGY LEVEL IS ARBITRARY. WE JUST TYPICALLY TAKE ZERO PE AT GROUND LEVEL. HOWEVER IT IS "DIFFERENCES' IN HEIGHT THAT COUNT FOR POTENTIALS.

thank you so much!

Understanding the concepts of kinetic and potential energy in roller coasters can be a bit confusing, but I'll do my best to explain it. Let's go through your example step by step:

1st Hill: With a height of 50 meters, the roller coaster gains potential energy (PE) because it is higher above the ground. At the very top of the first hill, the roller coaster will have maximum potential energy and zero kinetic energy (KE) because it hasn't started moving yet.

1st Drop: As the roller coaster goes down the first drop to a height of 10 meters, some of its potential energy is converted into kinetic energy. At the bottom of the drop, it will have gained some kinetic energy but will still retain some potential energy since it's not at ground level yet.

2nd Hill: As the roller coaster goes up the second hill to a height of 40 meters, it gains potential energy again. At the very top of this hill, most of the roller coaster's energy will be in the form of potential energy, but there will also be a small amount of kinetic energy due to the motion it gained during the first drop.

2nd Drop: As the roller coaster goes down the second drop to a height of 1 meter, most of its potential energy will convert back into kinetic energy. At the bottom of this drop, it will have mostly kinetic energy and a little bit of potential energy remaining.

3rd Hill: As the roller coaster goes up the third hill to a height of 45 meters, it gains more potential energy. Again, at the top of this hill, most of its energy will be in the form of potential energy, with a small amount of kinetic energy from the second drop.

Now, regarding your questions:

- The height of the hills does matter. The first hill needs to be the highest because it sets the maximum potential energy for the roller coaster. The subsequent hills may vary in height, but they will still contribute to the roller coaster's potential energy and affect its overall energy distribution.

- When there is a drop lower than the first drop (like the 2nd Drop and 1st Drop above), the potential energy from the first hill will indeed convert into kinetic energy during the first drop, even if the roller coaster doesn't reach the lowest point. The conversion of energy depends on the difference in height, and as long as there is a decrease in height, potential energy will convert to kinetic energy.

I hope this helps clarify the concepts of kinetic and potential energy in roller coasters!