Energy cannot be created or destroyed in any transformation. This powerful accounting principle helps us analyze everything from particle collisions, to the motion of pendulums.

The gravitational acceleration is \( g = 10 \text{ m/s}^2. \)

An object initially at rest is dropped, and starts to free fall. When the object is \( 60 \text{ m} \) above the ground, its velocity is \(10 \text{ m/s}. \) If the air resistance is negligible, from what height was the object dropped?

The gravitational acceleration is \( g = 10 \text{ m/s}^2. \)

The gravitational acceleration is \( g = 10 \text{ m/s}^2. \)

A roller-coaster initially at rest slides down a down-hill track, and then proceeds through a circular loop track of radius \(R=6\text{ m}.\) When the roller-coaster is at the highest point of the loop, it is traveling at the minimum speed required to stay on the track and not fall down. If the whole track is perfectly frictionless, what was the initial height \(h\) of the roller-coaster?

The gravitational acceleration is \(g=10\text{ m/s}^2.\)

The whole track is perfectly frictionless, and the gravitational acceleration is \(g=10\text{ m/s}^2.\)

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