Energy Something that enables an object to work is called energy. What are some different forms of energy? –Potential –Electrical –Mechanical –Kinetic

Potential Energy Potential Energy: energy that is stored and held in readiness to do work. Any substance that can do work has potential energy. –Fossil Fuels –Electric Batteries –Food

Potential Energy Work is required to elevate objects This potential energy is called –Gravitational Potential Energy (GPE) The amount of gravitational potential energy is equal to the work done against gravity by lifting it.

Energy is the physical agent that allows work to be done. Energy has many forms: –In motion (KE) –In position (GPE) –In the physical/chemical properties of materials (EPE) Energy, like work, is measured in Joules (J). AB Energy

Which path will take the most work to get the ball to the top of the tower?

Gravitational Potential Energy Work = Force x Distance Upward Force = weight –Work = Weight x Distance –Work = mg x Distance –GPE = mg x Distance (height) GPE = mgh

GPE Example The ball has a mass of 2kg, the tower is 3m tall. What is the GPE when the ball is on top of the tower? GPE = mgh

GPE Example The ball has a mass of 2kg, the tower is 3m tall. What is the GPE when the ball is on top of the tower? GPE = mgh

GPE Example The ball has a mass of 2kg, the tower is 3m tall. What is the GPE when the ball is on top of the tower? GPE = mgh

Which path will take the most work to get the ball to the top of the tower?

GPE Example A cannon fires a 10kg cannon ball 150m into the air. What is the GPE at its highest point? h=150m

GPE Example A cannon fires a 10kg cannon ball 150m into the air. What is the GPE at when the cannonball lands back on the ground?

Kinetic Energy Kinetic Energy: is the energy of motion Note that KE quadruples when the velocity doubles

30km/hr 60km/hr 120km/hr Skid 10m Skid 40m Skid 160m How far would a car skid?

Sample Problem #1 (KE) A train (m = kg) travels along a stretch of track with a velocity of 16m/s. Tunnel What is the KE of the train?

A train (m = kg) travels along a stretch of track with a velocity of 16m/s. How much work is required to stop the train in 84.6s?

A train (m = kg) travels along a stretch of track with a velocity of 16m/s. How much work is required to stop the train in 84.6s? Work-Energy Theorem

Elastic Potential Energy EPE: is the energy stored in a spring or flexible object k is the spring constant (Units N/m) (material dependent) –Which spring would be harder to compress? x is the distance compressed or stretched (Units m)

Compressing  When a spring is compressed from its neutral position, elastic potential energy is stored within the spring.  The energy required to compress a spring is given by Note: x is the displacement. x is the value of the number on the number line

Stretching  When a spring is stretched from its neutral position, elastic potential energy is stored within the spring.  The energy required to stretch a spring is given by

Sample Problem 3 (EPE) Consider a small toy dart gun. The dart is pushed 0.05m into the spring (k = 330N/m) within the gun. What is the EPE of the spring? Load

The Need For Algebra Some energy problems will require algebraic manipulation in order to be solved. Each energy equation can be broken down.

Conservation of Energy Example Recall the ball on top of the tower. What is the velocity of the ball if it falls from the tower?

Conservation of Energy Example What was the KE of the ball just before landing?

Energy was Conserved PE at the top of the tower KE at the bottom of the tower

The Law of Conservation of Energy The Law of Conservation of Energy: in a closed and isolated system, the total energy remains constant. –Energy can not be destroyed. –Energy transforms, but the total amount never changes.

What energy transformation take place in this example? Conservation of Energy

What energy transformation take place in this example? Conservation of Energy

What energy transformation take place in this example?

Conservation of Energy PE PE + KE KE PE + KE PE

Simple Harmonic Motion X1 X2 mgh 1 mgh 0 V=0

Hooke’s Law

The Law of Conservation of Energy In terms of the energy: In terms of the components:

Simple Harmonic Motion Simple Harmonic Motion: Motion caused by a linear restoring force that has a period independent of amplitude. Period: The time required to repeat one complete cycle Amplitude: Maximum displacement from equilibrium.

External Work ( W o ) You may have wondered what the W o term was for. W o is any work done by the system or on the system during an energy transition. In cases where energy is added to the system, W o is positive(+). Examples include motors and muscles. In cases where energy is lost by the system, W o is negative(-). Examples include friction and air resistance.

Kinetic Energy & Work-Energy Principle  Work-Energy Principle - the net work done on a body is equal to the change in its kinetic energy. Kinetic Energy Work Energy Theorem Units of W & KE Pronounced as a Joule

Conservation of Energy What are the kinetic and potential energies at the following points? Explain why. A B C

Conservation of Energy Example A car’s engine (m car = 1500 kg) puts 10,000 J of energy into getting the car to the top of a hill. Calculate the GPE & KE of the car at the three points below. h 3h/4 h/4 A B C

The MVE A statement of the conservation of energy that includes most of the forms of mechanical energy. KE GPE EPE RKE Energy BeforeEnergy After

Understanding the MVE - Launch  The projectile will be launched up from the ground. Key Factor What did the explosion do to the ball? Work-Kinetic Energy Principle? The net work done on a body is equal to the change in its kinetic energy.

Understanding the MVE – Free Fall Key Factor What is the ball’s final height? What is the ball’s GPE? The height is always equal to zero, and the GPE is always equal to zero at the Lowest Point.

MVE – Free Fall WS 11a #3 Find GPE of the ball at the surface of the table Find GPE of the ball at the top of the platform A beach ball is.82m above a picnic table which is.45m tall. The table is on a 2.9m platform.

Compressing

Understanding the MVE – Hoops, Anyone?

Conservation of Energy Example A ball, initially traveling at a velocity of 14m/s is rolled up a frictionless hill until it stops.. How high up the hill did it go?

Understanding the MVE - Archery Key Factor What was the GPE of the arrow just as it struck the target? Why? 8-25

Understanding the MVE – More Archery Let’s get a bulls eye hit this time! What was the GPE of the arrow at the beginning and the end of the arrow’s flight?

Understanding the MVE – In the Factory Key Factor What role did friction play in this problem? Friction resulted in the apparent loss of energy to the system. However, the energy is still accounted for as work other (W O ).

MVE – Archery WS Intro #3 An arrow (m=.15kg) is drawn back in a bow (k=1120N/m) a distance of.35m. What is the EPE? What is the GPE

Conservation of Energy Example Roller Coaster Down Hill Skier

Homework 11a #4 11b #2 11c #1-3 11d #1 11e #1,2

End CH 11

How far does it fall?  If the block slides a distance d down the plane, then how far does it fall at the same time?

Conservation of Energy Examples