Chapter 5, Unit 2: Kinetic & Potential Energy KEY

Legend Refresh & Connect Review of Work and Energy Two Major Categories Kinetic Energy Potential Energy Conservation of Energy Elastic Potential Energy

Refresh and Connect The amount of Work done on an object depends on: Force Change in Displacement Power is the rate at which work is done. Name one form of energy and an example of that energy.

Two Major Categories

Two Specific Forms of Mechanical Energy can be Kinetic Which is Energy in motion Potential Which can be Gravitational Elastic

Kinetic Energy is to Potential Energy The Ying to its Yang Ying is to Yang As Kinetic Energy is to Potential Energy

Kinetic Energy 𝐾𝐸= 1 2 𝑚 𝑣 2

Kinetic Energy = in motion Kinetic Energy happens only when an object is moving! The Kinetic Energy of an object depends on: The mass (m) The velocity (**must have) (v)

Scenario Practice: Identify the object that has the most Kinetic Energy and Why Scenario a Scenario B Object 2 b/c it has a greater velocity Object 2 b/c it has a greater mass m= 100 kg m= 50 kg v= 5 m/s 1 v= 8 m/s 1 2 v= 8 m/s v= 8 m/s 2 m= 100 kg m= 100 kg

Using the KE Equation Equation: 𝐾𝐸= 1 2 𝑚 𝑣 2 Where: KE Kinetic Energy m mass v velocity Example Problem: A 150 kg fat man is being chased by a 60 kg zombie. The man is running with a velocity of 3 m/s and the zombie with 4 m/s. Find the Kinetic Energy the zombie and the man.

Gravitational Potential Energy

Gravitational Potential Energy An object’s Gravitational Potential Energy depends on: The object’s mass (m) The object’s height from the ground (h) The acceleration due to gravity (g) Gravitational Potential Energy of an object increases as its height increases. Examples: Sky Scraper Ride Bungee Jumping Jumping on a trampoline

Practice: Circle the one that has the most Gravitational Potential Energy Scenario 1 Scenario 2 Balloon 2 b/c it has a greater mass Skier b/c it has a greater height 1 2

Using the GPE Equation Equation: 𝑃 𝐸 𝑔 =𝑚𝑔ℎ Where: PE Potential Energy m mass g acceleration due to gravity h height; distance from Zero Example Problem: The tower of terror in Disney World is 60 m tall. If the mass of the ride is 453 kg including its passengers, what is the potential energy of the ride before it begins its descent downwards? 𝑚=453 𝑔=10 𝑚 𝑠 2 h=60 m 𝑃 𝐸 𝑔 =? 𝑃 𝐸 𝑔 =𝑚𝑔ℎ 𝑃 𝐸 𝑔 = 453 10 60 𝑃 𝐸 𝑔 =271800 𝐽

Elastic Potential Energy

Elastic Potential Energy Elastic potential energy is resulted from stretching or compressing an object; depends on distance compresses or stretched Examples: Rubber Bands Springs Resistance Band Equation: 𝑃 𝐸 𝑒𝑙𝑎 = 1 2 𝑘 (∆𝑥 2 ) Where: 𝑃 𝐸 𝑒𝑙𝑎 →𝐸𝑙𝑎𝑡𝑖𝑐 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦=[𝐽] 𝑘→𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡=[N/m]*** 𝑥→𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑜𝑟 𝑠𝑡𝑟𝑒𝑡𝑐ℎ𝑒𝑑

Elastic Potential Practice Problem A 9 year old boy has a crush on a girl in his class. To get her attention he takes off on the rubber bands on his braces and stretches it back .03m. Calculate t the elastic potential energy of the rubber band before the boy releases is the spring constant equals 120 N/m. 𝑃 𝐸 𝑒𝑙𝑎 =? 𝑘=120 𝑁 𝑚 𝑥=.03𝑚 𝑃 𝐸 𝑒𝑙𝑎 = 1 2 𝑘 (∆𝑥 2 ) 𝑃 𝐸 𝑒𝑙𝑎 = 1 2 (120) .03 2 𝑃 𝐸 𝑒𝑙𝑎 =0.054 𝐽

Conservation of Energy

It’s the LAW! Law of Conservation of Energy states: Energy can neither be created nor destroyed. Instead it is converted from one form of energy to another Aka this means the Beginning must equal the End!

Process of Changing from Potential to Kinetic

An object can have both Potential and Kinetic Energy at the same time…but that amount can change quickly

Identify at each point if there is KE, PE, or Both All PE Both but more PE Both but more KE All KE All KE All KE

The Math of Conservation Initial Mechanical Energy = Final Mechanical Energy 𝑀 𝐸 𝑖 =𝑀 𝐸 𝑓 𝑃 𝐸 𝑔𝑖 + 𝐾𝐸 𝑖 =𝑃 𝐸 𝑔𝑓 + 𝐾𝐸 𝑓 𝑚𝑔 ℎ 𝑖 + 1 2 𝑚 𝑣 𝑖 2 =𝑚𝑔 ℎ 2 + 1 2 𝑚 𝑣 𝑓 2

Practice Problem #1 h=15m m=2kg g=10 m/s^2 v=? 𝑚𝑔ℎ= 1 2 𝑚 𝑣 2 Misael is standing on the 15m high roof of EHTHS with a 2 kg water balloon and sees Ms. Moody walking below. Seeing his opportunity to soak Ms. Moody he drops the balloon. Fortunately, Misael doesn’t have great aim and misses Ms. Moody and the balloon hits the ground next to her. With what velocity was the balloon moving at impact? h=15m m=2kg g=10 m/s^2 v=? 𝑚𝑔ℎ= 1 2 𝑚 𝑣 2 2𝑚𝑔ℎ=𝑚 𝑣 2 2𝑔ℎ =𝑣 𝑣= 2(10)(15) 𝒗=𝟏𝟕.𝟑𝟐 𝒎/𝒔

Practice Problem #2 h=? m=60kg g=10 m/s^2 v=7 m/s 𝑚𝑔ℎ= 1 2 𝑚 𝑣 2 A 60kg skate boarder is rolling on a flat horizontal surface with a velocity of 7 m/s right before he begins moving up the ramp. How high up the ramp will the skate boarder reach before he begins moving back down? 𝑚𝑔ℎ= 1 2 𝑚 𝑣 2 𝑔ℎ= 1 2 𝑣 2 ℎ= 1 2 𝑣 2 𝑔 = 1 2 7 2 10 𝒉=𝟐.𝟒𝟓 𝒎 h=? m=60kg g=10 m/s^2 v=7 m/s

Worksheet 2: #1: 24,000 J #2: 118 W