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## Potential Energy

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.

# Potential Energy Due to Gravity

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 $$g=10\text{ m/s}^2.$$

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 $$g=10\text{ m/s}^2.$$

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 $$g=10\text{ m/s}^2.$$

An old English nursery rhyme starts off "Jack and Jill went up the hill to fetch a pail of water". If the hill is 10 m high and Jack weighs 700 N, how much work in Joules did Jack need to do to get to the top of the hill?

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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