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Potential energy lets us do work in the present to change things in the future. If energy is currency, then potential energy is money in the bank.

A crate of mass \(m=4\text{ kg}\) slides down a frictionless inclined plane of length \(d=8\text{ m}\) that makes a \(30^\circ\) angle with the horizontal. What is the crate's change in gravitational potential energy when it reaches the bottom of the inclined plane?

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

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A \(6\text{ kg}\) object is dropped from the edge of a \(150\text{ m}\) high cliff. What is its gravitational potential energy (relative to the ground) after \(3\) seconds?

Ignore any air resistance and assume that gravitational acceleration is \(g=10\text{ m/s}^2.\)

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A \(80\text{ kg}\) man stands on the edge of a \(50\)-meter-high cliff. What is his gravitational potential energy relative to the ground?

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

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**in Joules** did Jack need to do to get to the top of the hill?

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An object of mass \(3\text{ kg}\) is dropped from a height of \(102\text{ m}.\) After \(2\) seconds, the object's gravitational potential energy is \(E_1,\) and \(4\) seconds after the drop it is \(E_2.\) Find the value of \(E_1+E_2.\)

The air resistance is negligible and the gravitational acceleration is \(g=10\text{ m/s}^2.\)

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