Objectives: The students Objectives: The students will be able to:will be able to:

Solve problems using the law of Solve problems using the law of conservation of energy.conservation of energy.

Analyze collisions to find the change Analyze collisions to find the change in kinetic energy.in kinetic energy.

• An object has the MOST kinetic energy when it’s movement is the GREATEST.

• When an object has the LEAST potential energy, it has the MOST kinetic energy.

A water bottle is knocked off a desk.When does the bottle have the MOST

kinetic energy?

A. At the top of the fall.B. In the middle of the fall. C. At the bottom of the fall.

• C. At the bottom of the fall.

• It has the most kinetic energy when its movement and speed are greatest, which is at the bottom of the

fall right before it hits the ground.

• When an object has the LEAST potential energy is when it has the MOST kinetic energy.

Roller Coasters• When does the train on

this roller coaster have the MOST potential energy?

• AT THE VERY TOP!• The HIGHER the train is lifted

by the motor, the MORE potential energy is produced.

• At the top of the hill the train has a huge amount of potential energy, but it has very little kinetic energy.

• As the train accelerates down the hill the potential energy is converted into kinetic energy.

• There is very littlepotential energy at the bottom of the hill, but there is a great amount of kinetic energy.

• When does the train on this roller coaster have the MOST kinetic energy?

(When is it moving the fastest?)(When does it have the LEAST

potential energy???)

• At the bottom of the tallest hill!

 The Conservation of Mechanical Energy

THE PRINCIPLE OF CONSERVATION OF

MECHANICAL ENERGY

The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external non-conservative forces is zero.

Conservation of Mechanical Energy

If friction and wind resistance are ignored, a bobsled run illustrates how kinetic and potential energy can be interconverted, while the total mechanical energy remains constant.

Mechanical Energy and Its Conservation

If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign.

This allows us to define the total mechanical energy:

And its conservation:

(6-12b)

Problem Solving Using Conservation of Mechanical Energy

In the image on the left, the total mechanical energy is:

The energy buckets (right) show how the energy moves from all potential to all kinetic.

Problem Solving Using Conservation of Mechanical Energy

If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height.

Rollercoaster Example

• Loss in height corresponds to a gain in speed as total energy is conserved.

Skier Example #1

• When the skier loses his total mechanical energy, work is done on the snow and the snow gains the energy.

A Daredevil Motorcyclist

A motorcyclist is trying to leap across the canyon shown in the Figure above by driving horizontally off the cliff at a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.

Now use a kinematic and vector approach to solve this.

Roller Coaster (Ideal)

The Magnum XL-200 at Cedar Point Park

In Sandusky, Ohio. The ride includes a vertical drop that accelerates the cart to a speed of 34 m/s (76 mi/hr) at the bottom of the dip. Assume that the coaster has a speed of nearly zero as it crests the top of the hill. Neglecting friction and other non-conservative forces, determine the approximate height of the peak.

Hint: Use the energy approach.

Non-conservative Forces for the Roller Coaster Example

In the roller coaster example, we ignored non-conservative forces, such as friction. In reality, however, such forces are present when the roller coaster descends.

Energy in a Roller Coaster Ride1. Go to the following site:

http://www.pbslearningmedia.org/resource/hew06.sci.phys.maf.rollercoaster/energy-in-a-roller-coaster-ride/

2. Run the animation and observe the relationship between kinetic and potential energy at each position.

3. Stop the roller coaster and at each position and describe on a sheet of paper the relationship between kinetic and potential energy using the pie chart. Then explain in detail why that relationship exists based on the information given in the animation.

4. Now you will design your own roller coaster. Go to the following site: http://www.learner.org/interactives/parkphysics/coaster/

5. Follow the directions on how to build your roller coaster. Think through each step carefully and the physics behind each step.

6. When you are finished you, will get an analysis of your design. On the back of the paper you used for the previous activity, explain why your steps were successful in terms of energy or why you were not successful and what needs to be done in order to improve your design.

Conservation of Energy Conservation of Energy ProblemProblem

Starting from rest, a child zooms Starting from rest, a child zooms down a frictionless slide from an down a frictionless slide from an initial height of 3 m. What is her initial height of 3 m. What is her speed at the bottom of the slide? speed at the bottom of the slide? (Assume she has a mass of 25 kg)(Assume she has a mass of 25 kg)

Conservation of Energy Conservation of Energy ProblemProblem

hhii = 3m = 3m m = 25kgm = 25kg vvii = 0 m/s = 0 m/s

hhff = 0m = 0m vvff = ? = ?• Slide is frictionless Slide is frictionless Mechanical energy is conserved Mechanical energy is conserved• Kinetic energy & potential energy = only forms of energy Kinetic energy & potential energy = only forms of energy

presentpresent• KE = ½ mvKE = ½ mv22 PEPEgg = mgh = mgh

• Final gravitational potential energy = zero (Bottom of the Final gravitational potential energy = zero (Bottom of the slide) slide) PE PEgfgf = 0 = 0

• Initial gravitational potential energy Initial gravitational potential energy Top of the slide Top of the slide PEPEgigi = mgh = mghii (25kg)(9.8m/s (25kg)(9.8m/s22)(3m) = 736 J)(3m) = 736 J

Conservation of Energy Conservation of Energy ProblemProblem

hhii = 3m = 3m m = 25kgm = 25kg vvii = 0 m/s = 0 m/s

hhff = 0m = 0m vvff = ? = ?• Initial Kinetic Energy = 0, because child starts at restInitial Kinetic Energy = 0, because child starts at rest

• KEKEii = 0 = 0

• Final Kinetic EnergyFinal Kinetic Energy• KEKEff = ½ mv = ½ mv2 2 ½ (25kg)v ½ (25kg)v22

ff

• MEMEii = ME = MEff

PEPEii + KE + KEi i = PE= PEff + Ke + Keff

736 J + 0 J = 0 J + (1/2)(25kg)(v736 J + 0 J = 0 J + (1/2)(25kg)(v22ff))

vvff = 7.67 m/s = 7.67 m/s

Elaboration

• Energy Transfer 11-3 Transparency

• Conservation of Energy Concept Development Page

• Conservation of Energy Lab

• Practice Problems p.297 #s 15, 17

• Practice Problems p.300 #s 19, 21

• Section Review p.301 #s 24, 27, 28

• Page 308 & 309 #s 73, 74, 77

Closure

• Kahoot 11.2