What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics.

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1 Bell Ringer Define Kinetic Energy, Potential Energy, and Work. What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics. Attempt to define momentum and explain what the conservation of momentum is to the best of your abilities.

2 NOTES 6.2: CONSERVATION OF ENERGY

3 Objectives: Differentiate among the various forms of energy and recognize that they can be transformed from on form to others. State the Law of Conservation of Energy Explore the Law of Conservation of Energy by differentiating among open, closed, and isolated systems and explain that the total energy in an isolated system is a conserved quantity. Calculate the spring potential energy using Conservation of Energy. Relate spring potential energy and gravitational potential energy to the total mechanical energy of a system using the conservation of energy. Relate the law of conservation of energy to a roller coaster ride.

4 Vocabulary: Gravitational Potential Energy Elastic Potential Energy Kinetic Energy Law of Conservation of Energy Energy lost due to friction Ramp

5 Active Physics Book: Chapter 2 Section 8: p (Potential & Kinetic Energy in the Pole Vault) Chapter 2 Section 9: p (Conservation of Energy: Defy Gravity) Chapter 4 Section 2: p (Elastic Potential Energy) Chapter 4 Section 3: p (Elastic Potential Energy)

6 Further Learning: Red Book in Class: Chapter 11 Section 1-2: p (Energy and its Conservation) Khan Academy: Conservation of Energy Physics Classroom: Work, Energy, and Power

7 Potential Energy (Recall): Potential Energy The energy of a body or a system with respect to the position or the arrangement of the particles of the system. An object can store energy as the result of its position. Potential Energy is somewhat of a poor word choice. To state it better, potential energy is really just the potential to do work. Think of it this way: I set a ball on top of a desk. We know full well that the ball may roll to the end and if it rolls to the end, it has the potential to fall. Whereas if it was on the floor, it no longer has the potential to fall further. We are making the floor our reference point in this scenario.

8 Potential Energy (Recall): Potential Energy can come in many different forms. Two of the most common are: 1. Gravitational Potential Energy: U g = mgh 2. Elastic Potential Energy (also known as Spring Potential Energy): U s = 1 2 kx2

9 Conservation of Energy: In an isolated system where only conservative forces can cause energy changes; the kinetic energy and potential energy can change, but their sum, the mechanical energy, E mec, of the system cannot change that is known as the Principle of Conservation of Mechanical Energy. E mec = K + U = 0 NOTE: The principle of conservation of mechanical energy allows us to solve problems that would be quite difficult to solve using only Newton s laws.

10 Conservation of Energy: IMPORTANT: When the mechanical energy of a system is conserved, we can relate the sum of kinetic energy and potential energy at one instant to that at another instant without considering the intermediate motion and without finding the work done by the forces involved. Law of Conservation of Energy the total energy E TOT of a system can change only by amounts of energy that are transferred to or from the system. CONSERVATION OF ENERGY: K i + U i = K f + U f

11 Conservation of Energy: K i + U i = K f + U f K i = initial kinetic energy U i = initial potential energy K f = final kinetic energy U f = final potential energy

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13 Sample Problem: 1. A 50 gram ball is attached to a spring with a spring constant of 120 N/m. If the spring is compressed by 10 cm, what will be the balls velocity when the spring is released? 2. During a hurricane, a large tree limb, with a mass of 22.0 kg and a height of 13.3 m above the ground falls on a roof that is 6.0 m above the ground. (a) Ignoring air resistance, find the kinetic energy of the limb when it reaches the roof. (b) What is the speed of the limb when it reaches the roof? (Use Conservation of Energy) (c) What is the speed of the limb when it reaches the roof? (Use constant acceleration equation)

14 Work done on a System by an External Force: Work is energy transferred to or from a system by means of an external force acting on that system. Positive Work A transfer of energy to a system. Negative Work A transfer of energy from a system.

15 Work done on a system, no friction involved: W = K + U W = E mec (Work done on system, no friction involved.) What this means is that any time there is any change in energy than work must have done on or by the system.

16 Power: Power is the rate at which energy is transferred by a force from one type (of energy) to another. Average Power: Instantaneous Power:

17 Sample Problem: 3. A bike rider approaches a hill at a speed of 8.5 m/s. The combined mass of the bike and the rider is 85.0 kg. Choose a suitable system. (a) Find the initial kinetic energy of the system. (b) Assuming there is no friction, at what height will the bike come to rest? (c) What is the total mechanical energy of the system? (d) How much work is done?

18 PHET Skate Park:

19 Exit Ticket: 1. You go to a water amusement park and try out several water slides. One slide is angled at 10 degrees to the horizontal and provides a straight shot to the pool whereas another is angled at 5 degrees and provides a graceful spiraling path to the pool. Both slides are of identical height and you can ignore friction. Which slide would you choose if you wanted to have the slowest traveling speed as you reached the end of the slide? Why? 2. When designing a roller coaster ride, what requirement (related to energy) must be enforced when designing the various hills and loops the carts will traverse through the ride? 3. You drop an object from a height of 1.5 meters. How far will the object fall before its kinetic energy equals its remaining gravitational potential energy?

20 Roller Coaster Problem: