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1 Chapter 4 Activity 2 GPE and KE

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2 Potential Energy Potential Energy: stored energy. There are many ways that energy can be stored and then released. It’s a lot like saving money in the bank so that it can be used later...

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3 Gravitational Potential Energy When an object is lifted to a particular height, the stored energy due to its elevated position increases. A dam is a good example of this.

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4 Gravitational Potential Energy Definition GPE = weight x height GPE = (mg) h GPE = mgh Mass [in kg] multiplied by the acceleration due to gravity (“g”: 9.8 m/s/s) is the object’s weight. The units of energy are [Joules].

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5 GPE Example: A crane lifts a steel beam with a mass of 2500 kg to a height of 20 m. How much gravitational potential energy does the beam have?

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6 GPE Example Use the mathematical definition of GPE: (You may round “g” to 10 m/s/s) GPE = (m g) h (2500kg * 10 m/s 2 )* 20 m 25,000 N * 20 m 500,000 J

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7 Reference Point, Base Level When measuring an “h” to calculate GPE, it’s important to know where you are measuring from (like the pendulum in lab). Any point can be used as a base level because the energy amount you calculate will be relative. However, you must be consistent.

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8 Kinetic Energy Kinetic Energy, KE: energy of motion KE = 1/2 m v 2 m = mass v = velocity Any object in motion has kinetic energy.

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9 Objects with a small mass can have high kinetic energy if their velocity is high. (Example: a bullet)

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10 Objects moving at slow speed can have great kinetic energy if their mass is great. (Example: a freighter)

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11 KE Example: Ex: A 80 kg sprinter may average about 10 m/s during a 100m dash. What would his KE be? KE = 1/2 mv 2 KE = 1/2 (80kg) (10m/s) 2 KE = 4000 kgm 2 /s 2 KE = 4000 J

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12 Conservation of Energy: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. P.E. K.E.

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13 For an object that drops, any energy “lost” is usually released in the form of heat energy due to friction. In any problems in class, we will assume that our roller coaster track is “frictionless”.

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14 At the top, the diver has all PE As he falls, PE is changed to KE. Before he hits, all the PE has changed to KE. Notice that the total amount of energy remains constant.

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15 Example: Question: If a 2 kg brick were to fall from a building 45 m high, how fast would it be traveling just before it hits the ground? 2kg

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16 Solution: GPE top = KE bottom mgh = mv 2 /2 (2kg) (10m/s 2 ) (45m) = (2kg) v 2 /2 notice “m” cancels out (10m/s 2 ) (45m) = v 2 /2 450 m 2 /s 2 = v 2 /2 900 m 2 /s 2 = v 2 v= 30 m/s

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Graphing of Lab Data GPE top = KE bottom mgh = mv 2 /2 gh = v 2 /2 v 2 = (2g) h If there was no friction, your lab data should have given you a slope of 19.6 m/s/s (this is 2g!) Which set of lab data was closest? –Pendulum, Low or High Angle Tracks? 17

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