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Energy Chapter 5 Section 2

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What is Energy? Energy – A scalar quantity that is often understood as the ability for a physical system to produce changes on a different physical system. Units for energy is a “Joule” The variable for a Joule is a capital “J”

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Kinetic Energy Kinetic Energy – The energy of an object due to it motion. Kinetic energy depends upon the object’s velocity and mass. Any mass that is moving has kinetic energy.

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**Equation for Kinetic Energy**

KE = ½mv² Kinetic Energy = ½ x mass x (velocity)² Given the objects velocity and mass, the energy that the object has can be calculated using the formula above.

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Example Problem A car traveling at 50m/s has a mass of 1000kg. Calculate the kinetic energy.

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**Example Answer KE = ½mv² = ½ (1000kg) (50m/s) ² =1,250,000**

KE = 1,250,000J

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Potential Energy Potential Energy – The energy associated with an object due to its position. In other words, potential energy is stored energy that has the potential to move because of its position with respect to some other location.

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**Different Forms of Potential Energy**

There are two different forms of potential energy: Gravitational Potential Energy Elastic Potential Energy

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**Gravitational Potential Energy**

Gravitational Potential Energy – Potential energy associated with an object due to its position relative to the Earth or some other gravitational source.

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**Gravitational Potential Energy Equation**

PEg = mgh Gravitational Potential Energy = mass x free-fall acceleration x height

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**Converting Gravitational Potential Energy into Kinetic Energy**

Imagine a rock falling off a cliff. As it falls, it gains kinetic energy since it picks up velocity as it falls to the ground below. But where does the kinetic energy come from? It comes from the gravitational potential energy that is associated with the rock’s initial position on the cliff relative to the ground below.

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**Origin of Gravitational Potential Energy**

Gravitational potential energy is a result of an object’s position, so it must be measured relative to some ZERO level. Doesn’t matter where you place the zero level (origin), but it must remain consistent through out the problem.

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Example Problem How much potential energy does a rock have that has a mass of 10kg and is 100m off the ground on top of a cliff?

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**Example Problem Answer**

PEg = mgh =(10kg)(9.8m/s²)(100m) =9800J PEg = 9800J

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**Elastic Potential Energy**

Elastic Potential Energy – The potential energy in a stretched or compressed elastic object. Examples: Springs Rubber bands Shocks

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**Relaxed Length of a Spring**

The length of a spring when no external forces are acting on it is called the relaxed length of a spring. When an external force compresses or stretches a spring, elastic potential energy is stored in the spring.

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**Elastic Potential Energy Equation**

PEelastic = ½kx² Where: Elastic Potential Energy – PEelastic k – Spring Constant x – Distance compressed or stretched

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Spring Constant Spring Constant – A parameter that expresses how resistant a spring is to being compressed or stretched. For a flexible spring the constant is small and for a stiff spring the constant is large. The units for the spring constant is “N/m”

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Example Problem A child has a rubber band with a length of 0.10m. The child pulls back on the rubber band to a distance of 0.20m. The spring constant of the rubber band is 5 N/m. What is the potential energy with in the rubber band?

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**Example Problem Answer**

PEelastic = ½kx² = ½ (k) (xf – xi)² = ½ (5 N/m) (0.20m – 0.10m)² = ½ (5 N/m) (0.10m)² =0.025J PEelastic = 0.025J

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Mechanical Energy Mechanical Energy – The sum of kinetic energy and all forms of potential energy. Example: Any kind of mechanical device Clocks Air compressor Basically anything that has moving pieces… Doesn’t include electrical, chemical, or heat energy.

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**Mechanical Energy Equation**

ME = KE + ΣPE ME = Mechanical Energy KE = Kinetic Energy ΣPE = The sum of all the potential energy

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**Classification of Energy**

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