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Chapter 4 Activity 2GPE and KE

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Potential EnergyPotential 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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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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Gravitational Potential Energy Definition

GPE = weight x heightGPE = (mg) hGPE = 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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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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GPE ExampleUse the mathematical definition of GPE:

(You may round “g” to 10 m/s/s)

• GPE = (m g) h• (2500kg * 10 m/s2)* 20 m

• 25,000 N * 20 m• 500,000 J

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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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Kinetic Energy

Kinetic Energy, KE: energy of motion

KE = 1/2 m v2

m = mass v = velocity

Any object in motion has kinetic energy.

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Objects with a small mass can have high kinetic energy if their velocity is high.

(Example: a bullet)

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Objects moving at slow speed can have great kinetic energy if their mass is great.

(Example: a freighter)

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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 mv2

KE = 1/2 (80kg) (10m/s)2

KE = 4000 kgm2/s2

KE = 4000 J

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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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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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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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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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Solution: GPEtop = KEbottom

mgh = mv2/2(2kg) (10m/s2) (45m) = (2kg) v2/2

notice “m” cancels out(10m/s2) (45m) = v2/2

450 m2/s2 = v2/2900 m2/s2 = v2

v= 30 m/s

Graphing of Lab Data• GPEtop = KEbottom

• mgh = mv2/2• gh = v2/2• v2 = (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?

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