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**Kinetic and Gravitational Potential Energy**

Learning Goal 5.1: Identify, define, and calculate kinetic and gravitational potential energy.

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What is Energy? Energy is a tricky concept to put our finger on… it’s one of those things that we KNOW is there and that we can see and measure. Part of why energy is so hard to define is because it can take so many different forms… kinetic, potential, electrical, thermal, chemical, magnetic, nuclear, light, sound… eek! For now, let’s go with the following definition: Energy is the ability to cause change.

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Basics of Energy Energy can be mechanical (related to things moving) or non-mechanical… we’ll focus on the mechanical forms for now. There are two types of mechanical energy: Kinetic (when things are moving) Potential (when things have potential to move) Regardless of the form it takes (kinetic, potential, sound, thermal, nuclear, etc.), energy is measured in Joules (J). Energy is a scalar, not a vector (it has no direction)!

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**KE = ½ mv2 Kinetic Energy Kinetic energy: energy due to motion**

An object that’s moving always has kinetic energy! We calculate kinetic energy this way: KE = ½ mv2 KE = kinetic energy (J) m = mass (kg) v = speed (m/s)

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Sample Problem A 1200 kg sports car traveling down the road has 375,000 J of kinetic energy. How fast is it moving? m = 1200 kg KE = 375,000 J v = ? KE = ½ mv² 375,000 J = ½ (1200 kg) (v)² v² = 625 m²/s² v = 25 m/s

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**Potential Energy Potential energy: stored energy based on position**

An object has potential energy if it’s placed in a position where it has the potential to move Two types: Gravitational potential energy: PE due to gravity Elastic potential energy: PE due to stretching or compression (like in a spring or a rubber band) For now, we’ll be focusing on gravitational potential energy

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**Gravitational Potential Energy**

Gravitational PE: PE due to gravity We calculate gravitational potential energy using: PE = mgh PE = gravitational potential energy (J) m = mass (kg) g = 9.8 m/s2 [on Earth] h = height above reference level (m)

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Sample Problem A woman with a mass of 60 kg climbs a set of stairs that are 3 m high. How much gravitational potential energy does she gain as a result of the climb? m = 60 kg h = 3 m g = 9.8 m/s² PE = mgh PE = (60 kg) (3 m) (9.8 m/s²) PE = 1764 J

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