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One conservation of energy practice problem involves a roller coaster at the top of a hill. If the roller coaster has a potential energy of 1000 J at the top of the hill and a kinetic energy of 200 J at the bottom, what is the total mechanical energy of the roller coaster system?

To solve this problem, you can use the conservation of energy principle, which states that the total mechanical energy of a system remains constant if only conservative forces are acting on it. In this case, the roller coaster system only experiences gravitational potential energy and kinetic energy.

At the top of the hill, the roller coaster has 1000 J of potential energy. At the bottom, it has 200 J of kinetic energy. Therefore, the total mechanical energy of the roller coaster system is:

Total mechanical energy Potential energy Kinetic energy Total mechanical energy 1000 J 200 J Total mechanical energy 1200 J

So, the total mechanical energy of the roller coaster system is 1200 J. This practice problem helps illustrate how energy is conserved in a system and how potential and kinetic energy are related.

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