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Unit 5-2: Energy

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Mechanical Energy When mechanical work is done, mechanical energy is put into or taken out of an object. Mechanical energy is a measurement of the ability of a machine to do work. Like work, energy is measured in Joules.

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Mechanical Energy The focus of this unit will be two types of mechanical energy. Potential Energy Kinetic Energy There are other types of energy out there that can come from work, but they will not be the focus of this unit.

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Potential Energy Energy that is stored and held in readiness is called potential energy. Potential energy can be obtained by moving an object to a higher position, in a chemical form, in a spring, etc. We will be focusing on two types of potential energy: Gravitational Potential Energy Spring Potential Energy

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Gravitational Potential Energy Work is required to move an object against the earth’s gravity. As this work is done, the object that was moved vertically gains potential energy. Water in a water tower has gravitational potential energy because it was lifted off the ground.

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Gravitational Potential Energy It doesn’t mater how the object is moved up to a certain height, just the vertical displacement is the important part. Remember the work is done against gravity, which is a vertical force. Lowering an object decreases its gravitational potential energy.

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Gravitational Potential Energy The amount of gravitational potential energy (GPE) possessed by an object is determined by multiplying the weight of an object by its height from the base. GPE = weight x height GPE = mass x gravity x height GPE = mgh Potential energy is not a vector, so there is no sign on it.

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Spring Potential Energy By compressing a spring, energy is stored in it. This is another form of potential energy. Since springs can be made of different materials, each spring has a different ‘spring constant’ When the energy stored in the spring is released, the spring decompresses.

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Spring Potential Energy Work is normally done against the spring to compress it This means that the direction of work is negative because the spring must be compressed opposite of the direction the spring will be pointing.

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Spring Potential Energy Spring Potential Energy (SPE) can be calculated by multiplying half the spring constant (determined by the type of material in the spring) and the amount of compression squared. SPE = 1/2 x Spring Constant x (Compression distance) 2 SPE = 1/2kx 2 K is the spring constant determined by the spring type. K is measured in N/m or kg/s 2

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Examples Example 1: A 30kg boulder is pushed up a 0.036km high hill. Determine the potential energy. Example 2: A crane pulls a 400N load up a distance of 18.3m. Determine the potential energy. Example 3: An 825kg crate is lifted up a vertical distance of 23506cm. Determine the potential energy.

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Examples Example 4: A spring is compressed by 0.13m and has a spring constant of 1.5N/m. Determine the potential energy the spring has. Example 5: If a spring gains 80J of energy when being compressed by 0.2m, determine the spring constant.

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Kinetic Energy When an object is in motion, it has energy as well. This energy of motion is known as kinetic energy. Kinetic Energy is dependent on the mass of an object and how fast it is going.

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Kinetic Energy Kinetic Energy (KE) is determined by taking half the mass of the object times its velocity squared. Since the velocity is squared, KE is ALWAYS positive. However, when solving for the velocity, it is up to you to determine whether or not it is positive or negative.

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Kinetic Energy KE = 1/2 x Mass x Velocity 2 KE = 1/2mv 2 Both mass and velocity affect an object’s energy, however the velocity has a much greater impact on the energy since it is squared.

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Examples Example 1: A car (1250kg) revs the engine and accelerates to a top speed of 18m/s. Determine the car’s kinetic energy. Example 2: An archer pulls an arrow (0.14kg) on a bow and lets it fly. If the arrow flies at 98m/s, determine its kinetic energy. Example 3: A 400g rock is thrown with 200J of energy, determine its velocity.

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