16 April, 06:43

# Suppose that you and two classmates are discussing the design of a roller coaster. One classmate says that each summit must be lower than the previous one. Your other classmate says this is nonsense, for as long as the first one is the highest, it doesn't matter what height the others are. What do you say

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1. 16 April, 07:03
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The second classmate is right: as long as the first one is the highest, it doesn't matter what height the others are.

This is because of the conservation of energy. The cart starts a rest in the first summit, so it has only potential energy m*g*h, being h the height of the first summit. The cart cannot reach a higher summit with height h' > h, because it has not enough energy. The potential energy at height h' is higher than its potential energy.

But, as long as there is no friction, the cart can reach any summit lower than the first one, because it has enough available potential energy.
2. 16 April, 08:18
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The other classmate is right.

Explanation:

As long as the first one is the highest, it does not matter what height are other hills or peak as energy is conserved during its motion.