Potential and Kinetic Energy Energy: is the ability to do work Work is being done whenever some physical force is being used to move an object some distance

Energy means that birds can fly, tigers can roar, wind can blow, sun can shine, cars can go fast, factories can make things, light bulbs can glow and your computer can work. Without energy, there would be nothing: no life, no movement, no light, … nothing

Energy All objects contain energy in one form or another Can take the form of Motion -Sound Position - Electricity Heat Light It can never be destroyed It can only be converted from one form to another

Kinetic Energy = the energy an object possesses because of its motion The amount of Kinetic energy is dependent on the mass of the object in motion and it’s velocity.

Calculating kinetic energy If we know the mass of an object and its velocity we can determine the amount of kinetic energy possessed by using the following formula: kinetic energy = 1/2 (mass of object)(velocity of object)2 or KE = 1/2 mv2 or KE = 0.5mv2 The SI unit for kinetic energy is the Joule (J). A Joule is kg • m2/s2

A bicycle with a mass of 14 kg traveling at a velocity of 3 A bicycle with a mass of 14 kg traveling at a velocity of 3.0 m/s east has how much kinetic energy? KE = 0.5mv2 = 0.5(14 kg)(3.0 m/s)2 = 0.5(14 kg)(9.0 m2/s2) = 63 kg• m2/s2 = 63 J

A 1200 kg automobile is traveling at a velocity of 100 m/s northwest A 1200 kg automobile is traveling at a velocity of 100 m/s northwest. What is the kinetic energy of the automobile? KE = 0.5 mv2 = 0.5(1200kg)(100 m/s)2 = 0.5(1200 kg)(104 m2/s2) = 6 x 106 kg  m2/s2 = 6 x 106 J

VELOCITY = the measure of how fast an object is traveling in a certain direction! Velocity = distance ÷ time Distance = meters Time = seconds

Objects "tend to keep on doing what they're doing" In fact, it is the natural tendency of objects to resist changes in their state of motion. Without some outside influence, an object in motion will remain in motion and an object at rest will remain at rest.

Cardboard and a Coin placed on an Empty Tumbler Flick the cardboard with the finger. What do you observe? The coin drops into the tumbler. When we flick the cardboard the cardboard moves fast whereas the coin continues in its state of rest and hence drops into the tumbler.                                                                                                                                                                      This tendency to resist changes in their state of motion is described as inertia Cardboard and a coin placed on an empty glass Flick the cardboard with the finger. What do you observe? The coin drops into the tumbler. When we flick the cardboard the cardboard moves fast whereas the coin continues in its state of rest and hence drops into the glass. So it is clear that objects continue to remain in their state of rest or of uniform motion until an external force is applied.

Examples of Inertia of Rest A passenger standing in a bus leans backwards when the bus starts all of a sudden Fruits fall down when the branches of a tree are shaken Dust particles on a carpet falls when we beat the carpet with a stick Examples of Inertia of Motion A passenger standing in a moving bus leans forward when the bus stops all of a sudden A man carelessly stepping out of a moving train onto the ground leans forward Example of Inertia of Direction The water particles sticking to the cycle tire are found to fly off tangentially Inertia of a body depends upon its mass. That is, massive objects possess more inertia than lighter ones.

Galileo’s idea of inertia - 1 - A balled rolled down an incline would continue up the second incline at equal angle until the force of gravity forced it back down 2 – A ball rolled down the first incline would roll farther up the second incline since the angle is not as steep. 3 – A balled rolled down the inline would continue to roll indefinitely on the second plane since it would not be affected by gravity

Potential Energy The energy of position The amount of energy contained in an object at rest

Determining Potential Energy By its position and its weight (mass X gravity) PE = (mass)(gravity)(height) = mgh where m is mass in kg g is the force of gravity = 9.8 m/s2 h is the height The SI unit that represents potential energy is the Joule (J) (kg m2/s2).

Examine an example of potential energy A flower pot with a mass of 15 kg is sitting on a window sill 15 meters above the ground. How much potential energy does the flower pot contain? PE = (mass)(gravity)(height) = (15 kg)(9.8 m/s2)(15 m) = 2205 kg • m2/s2 = 2205 J = 2000 J = 2.2 x 103J

Examine an example of potential energy If the flower pot is lowered to a window sill that is 10. m from the ground. Does this change the potential energy of the flower pot? PE = (mass)(gravity)(height) = (15 kg)(9.8 m/s2)(10. m) = 1470 kg  m2/ = 1470 J = 1.5 x 103J

Potential or Kinetic Energy? Moving car Tree branch Bent car fender Balloon filled with air Balloon squirting around room Person inside a moving car

What type of energy does the space shuttle have at lift off?

Conversion of Potential to Kinetic Energy In this picture both kinds of energy are evident. Can you point them out?

The water at the top has potential energy When water falls to a lower level, the potential energy is converted to kinetic energy.

Velocity & Acceleration Some Review

Defining Velocity Kinetic energy was KE=1/2 (mass) (velocity)2 Describes both the rate and direction of the motion If an object speeds up or slows down in the given direction we say there is a change in velocity

VELOCITY AND SPEED Velocity is a measure of how fast an object is traveling in a certain direction. Example: A bus traveling 15 m/s increases its speed to 20 m/s The speed changed so the velocity changed The bus changes direction and goes east. Since the direction changed, so did the velocity

Car on a circular track = may have constant speed, but cannot maintain a constant velocity as it’s direction is always changing.

VELOCITY AND SPEED Speed is a measure of how fast something is moving, but there is not a directional element to it Is the distance on object moves per time or how fast something is moving without direction Speed = Distance ÷ Time (S=D ÷ T) If speed changes, so does the velocity

VELOCITY Velocity = distance ÷ time The units we use are m/s and d is distance.

ACCELERATION Acceleration is the change in velocity per unit of time. An example of this is when you travel in your car. Your velocity is not constant throughout the entire trip as you slow down and speed up as necessary. A positive acceleration means that you are speeding up and a negative acceleration means that you are slowing down.

ACCELERATION Acceleration has the formula: Acceleration = (Final Velocity) – (initial velocity) (Final time) – (Initial time) OR (time it takes to change velocity) A = vf – vi = ∆v ∆ means “change in” tf – ti ∆t Acceleration has the units of (distance unit)/(time unit) Ex: m/s2 or mi/h2

ACCELERATION Example acceleration problems Calculate the acceleration of an object with: Initial Velocity : 0.0m/s Final Velocity: 14m/s Time 4.0s A = 14m/s – 0.0m/s 4.0s A = 3.5m/s2

ACCELERATION A car stops from a velocity of 55m/s in 15 seconds. What is the cars acceleration? Is the car speeding up or slowing down? A = 0 – 55m/s -55m/s 15 s 15s A = -3.7m/s2 Car is slowing down