Mechanical EnergyEureka : http://www.youtube.com/watch?v=7K4V0NvUxRg

Gravitational Potential Energy•The energy possessed by an object because of its position relative to a lower position

•The potential of an object to be pulled down by gravity

A GPE Machine

Eg = mghEg – gravitational potential energy (J)m – mass (kg)g – gravitational field strength (N/kg, m/s2)h – height above reference level (m)

Compare with Work for lifting something

•We always have to indicate a reference level

Ex. The gravitational potential energy is 30J relative to the Earth’s surface

Example 1A 58 kg skydiver stands in the door of a plane preparing to jump. If the earth is 2.8 km below the skydiver, what is the skydiver’s potential energy relative to the earth?

Example 2A 10.0kg rock is on top of a house 5.00m high on the edge of a cliff 20.0m high. What is the gravitational potential energy of the rock relative toa) the roof of the house?b) the floor of the house?c) the bottom of the cliff?

Example 2 Cont’da) The h=o is at the top of the house.

Eg mgh

(10.0kg)(9.81N /kg)(0m)0J

relative to the top of the house. b) The h=0 is the floor of the house.

Eg mgh

(10.0kg)(9.81N /kh)(5.00m)490J

relative to the floor of the house. c) The h=o is at the bottom of the cliff.

Eg mgh

(10.0kg)(9.81N /kg)(25.0m)2450J

2.45 103J

relative to the bottom of the cliff.

Kinetic Energy•the energy possessed by an object due to its motion

Calculating Kinetic Energy:Ek = ½ mv2

Ek – Kinetic Energy (J)m – mass (kg)v – Speed (m/s)

Example 1What is the kinetic energy of a 60 g tennis ball that has a speed of 3.6 m/s?

Example 2What is the kinetic energy of a 6.0kg curling stone sliding at 4.0m/s?

Given: m=6.0kg, v=4.0m/s

E k 12mv2

12

(6.0kg)(4.0m /s)2

48J

Example 3What is the speed of a 5.44kg shotput if its kinetic energy is 68J?Given: m=5.44kg, Ek=68J

E k 12mv2

v 2 2E km

2(68J)5.44kg

25m2

s2

v 5.0m /s

Potential and Kinetic EnergySnowboarding• http://www.youtube.com/watch?v=58YvhpxXaN0

Mechanical Energy•The sum of the gravitational potential energy and the kinetic energy

•Think of TOTAL energy of an object due to it’s motion/position

•Mechanical energy will always stay the same unless WORK is done

•Ex. When a parachutist jumps from a plane, she initially has a large GPE and no kinetic energy. As she falls, she speeds up as her GPE converts to kinetic energy

Her Mechanical Energy will always be the same

Calculating Mechanical EnergyEm = Eg + Ek

Ek – Kinetic Energy (J)Eg – Gravitational Potential

Energy (J)Em – Mechanical Energy (J)

Example 1A boy has a stationary 5.1kg ball in his hand 3.2m off the ground. a) Calculate the Ek, Ep and Em of the ball

He then drops the ball,b) Calculate the speed when it drops 1.2 m

using the five constant acceleration equations.

c) Using the value from b) calculate Ek, Ep and Em of the ball at this point

Applications of Mechanical Energy•South African vultures eats bones – if they are too big the bird will drop them from a greater height so they break

Applications of Mechanical Energy•A roller coaster on a track – the height of

the first hill has to be high enough giving a high potential energy – this will be converted into kinetic energy which will make it go really fast

Top Thrill Dragster – Cedar Point, Ohio

•128 m tall, 193 km/h on the up and down

Energy Skate Park: BasicsComplete the PHeT Intro to Energy Lab (instructions on class site)

http://phet.colorado.edu/en/simulation/energy-skate-park-basics

Practice ProblemsPractice Problems posted on class site.

Extra HelpEverything you need to know from this lesson:• http://www.youtube.com/watch?v=iYEWIuQBVyg

Other Eureka Videos:http://youtu.be/BGmUVoX5s58

http://youtu.be/Tji6PDBck_8