M.I.T. C.P. Physics ENERGY

Energy is the ability to do work. Work = Force X Distance X cosΘ What is Energy? Energy is the ability to do work. Work = Force X Distance X cosΘ

Types of Energy Kinetic Energy Energy of Motion KE = ½ mv^2

Lab: Validating the KE Formula Interactive

Lab: Validating the KE Formula Data Chart Trial # KE (J) Mass (kg) Time (s) Distance (m) 1 2 3 4 5

Lab: Validating the KE Formula Calculation Chart Trial # Velocity (m/s) 1 2 3 4 5

Lab: Validating the KE Formula Analysis Chart Trial # KE (J) 1/2mv^2   1 2 3 4 5

Theoretical Physics

Calculate the kinetic energy of a 750-kg car moving at 13.9 m/s. Sample Problem 1 Calculate the kinetic energy of a 750-kg car moving at 13.9 m/s. Step 1 KE = ½ mv^2 Step 2 KE = ½ (750)(13.9)^2 Step 3 KE = 7.2 x 10^4J

What is the kinetic energy of the car if the speed is doubled? Sample Problem 2 What is the kinetic energy of the car if the speed is doubled? Step 1 KE = ½ mv^2 Step 2 KE = ½ (750)(27.8)^2 Step 3 KE = 3.0 x 10^5J

Sample Problem 3 How much work must be done to double the speed of the car? Work = Force X Distance X cosΘ The metric unit for KE = joules. The metric unit for work = joules.

Work Energy Theorem Work must be done to speed up the car or slow down the car. As the speed of the car changes, so does its KE. Work = ΔKE

How much work must be done to double the speed of the car? Sample Problem 3 How much work must be done to double the speed of the car? Step 1 W = ΔKE Step 2 W = (3.0 x 10^5)-(7.2 x 10^4) Step 3 W = 2.2 x 10^5J

Stored Energy or Energy of Position Types of Energy Potential Energy Stored Energy or Energy of Position

Types of Potential Energy Chemical Potential Energy

Types of Potential Energy Electrical Potential Energy

Types of Potential Energy Elastic Potential Energy Elastic Potential Energy = ½ kx^2

Types of Potential Energy Gravitational Potential Energy Gravitational Potential Energy = mgh

Sample Problem A 150-kg Humpty Dumpty sat on a 2.5 meter wall. What is Humpty Dumpty’s potential energy before his great fall? Step 1 PE = mgh Step 2 PE = (150)(9.8)(2.5) Step 3 PE = 3700J

Law of Conservation of Energy Energy can not be created nor destroyed, only changed. The total energy of a system remains constant.

Energy Conversion Total Mechanical Energy = PE + KE As the boy swings down, his PE decreases while his KE increases.

Energy Conversion Total Mechanical Energy = PE + KE As the boy swings down, his PE decreases while his KE increases. As the boy swings up, his PE increases while his KE decreases.

Interactive

Sample Problem A D B E C F

Lab: Conservation of Energy Interactive

Lab: Conservation of Energy Data Chart Height (m) PE (J) KE TME 6 5 4 3 2 1

Sample Problem A 7.26-kg bowling ball is dropped from a height of 2.5 meters into a toilet. What speed will the bowling ball hit the water? Step 1 PE = mgh Step 2 PE = (7.26)(9.8)(2.5) Step 3 PE = 180 J

Sample Problem A 7.26-kg bowling ball is dropped from a height of 2.5 meters into a toilet. What speed will the bowling ball hit the water? Step 4 PE = KE = ½ mv2 Step 5 180J = ½ (7.26)v^2 Step 6 V = 7.0m/s

Sample Problem Check A 7.26-kg bowling ball is dropped from a height of 2.5 meters into a toilet. What speed will the bowling ball hit the water? Step 1 D = ½ gt^2 Step 2 2.5 = ½ (9.8)t^2 Step 3 t = .71s

Sample Problem Check A 7.26-kg bowling ball is dropped from a height of 2.5 meters into a toilet. What speed will the bowling ball hit the water? Step 4 v = gt Step 5 v = (9.8)(.71) Step 6 v = 7.0m/s

Introduction to Engineering

Conservation of Energy Roller Coaster Physics

Lab: Roller Coaster Challenge Interactive

Lab: Roller Coaster Challenge Objectives The coaster must finish the whole course! Determine the fastest and slowest time possible to complete the course.

Lab: Roller Coaster Challenge Data Chart Fastest Time Slowest Time

Roller Coaster Design Kingda Ka 200 km/h 3.5 seconds 20,800 hp $25,000,000

Roller Coaster Physics

G Force

Roller Coaster Physics

Roller Coaster Physics

Roller Coaster Physics

Lab: More Thrills with Fewer Ills!

Lab: More Thrills with Fewer Ills!

Lab: More Thrills with Fewer Ills! Calculation Chart Values Standard Loop Chothoid Loop PE1 v1 KE1 TME1 TME2 v2 Ac G Force1 TME3 v3 29.73 m/s G Force2

Introduction to Engineering

Elasticity

Elasticity A material’s ability to return to its original shape after being deformed.

Vocabulary

Change in shape of an object. Deformation Change in shape of an object.

Strain

Applied Force / Original Area Stress Applied Force / Original Area

Types of Stress Tension-Compression

Types of Stress Shear

Types of Stress Hydrostatic

Stress Strain Curve

Elastic Limit

Youngs’ Modulus

Hooke’s Law F = kx k = Spring Constant

Lab: Special “k”

Not This Special “K”

Lab: Special “k” Data Chart Spring # Length 1 (m) Force (N) Length 2 1 3 4 5 6

Lab: Special “k” Conversion Formulas Centimeters to Meters cm/ 100 = m Grams to Newtons g/1000 x 9.81 = N

Lab: Special “k” Calculation Chart Spring # Force (N) ΔX (m) K (N/m) 1 2 3 4 5 6

Sample Problem A 0.50 newton weight is dropped onto a spring causing it to compress .46 m. Calculate k. Step 1 F = kx Step 2 0.50 = k (.46) Step 3 k = 1.1 N/m

Sample Problem 2 A 4kg block slides across a frictionless table with a velocity of 5m/s into a spring with a stiffness of 2500N/m. How far does the spring compress? Step 1 ½ mv^2 = ½ kx^2 Step 2 50J = ½ (2500) x^2 Step 3 X = .2 meters

Stress Strain Curve

Ultimate Stress

Lab: Ultimate Stress