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## Worked example 5.4: Roller coaster ride

Question: A roller coaster cart of mass starts at rest at point , whose height off the ground is , and a little while later reaches point , whose height off the ground is . What is the potential energy of the cart relative to the ground at point ? What is the speed of the cart at point , neglecting the effect of friction?

Answer: The gravitational potential energy of the cart with respect to the ground at point is

Likewise, the potential energy of the cart at point is

Hence, the change in the cart's potential energy in moving from point to point is

By energy conservation, , where represents kinetic energy. However, since the initial kinetic energy is zero, the change in kinetic energy is equivalent to the final kinetic energy . Thus,

Now, , where is the final speed. Hence,

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Richard Fitzpatrick 2006-02-02