Unit 4 - Work and Energy

Unit 4 - Work and Energy Chapter 6

Part 2 Conservation of Energy

Conservative vs. Nonconservative Forces • Conservative force – total Work on a closed path is zero. (ex: gravity) • Nonconservative force– total Work on a closed path is NOT zero. (ex: friction) Gravity- down Motion- up Gravity- down Motion- down -W +W Friction - right Motion- left -W Friction – left Motion - right -W Energy

Conservation of Energy • Law of Conservation of Energy – Energy cannot be created or destroyed, only converted from one form to another. • This means the amount of energy when everything started is still the amount of energy in the universe today! (Just in different forms!)

Conservation of Mechanical Energy • If non-conservative forces are NOT present (or are ignored) the total Mechanical Energy initially is equal to the total Mechanical Energy final. OR

Conservation of Mechanical Energy • Rearranged to other forms: OR • Use your brain instead of thinking about a formula! These are all just the concept “conservation of energy”

Conceptual Example 1: Pendulum • Pendulum - Kinetic and Potential Energy • In the absence of air resistance and friction… • the pendulum would swing forever • example of conservation of mechanical energy • Potential → Kinetic → Potential and so on… • In reality, air resistance and friction cause mechanical energy loss, so the pendulum will eventually stop.

Conceptual Example 2: Roller Coaster • Roller Coaster - Kinetic and Potential Energy

With Non-Conservative Forces… • If non-conservative forces (such as friction or air resistance) ARE present: • Be careful: Work done by friction is always negative! (Friction always opposes the motion) • So if friction is present, there is mechanical energy loss. (The energy is converted into heat and sound.)

With Non-Conservative Forces… • Rearranging the formula: OR

Conceptual Example 3: Downhill Skiing • Downhill Skiing - Kinetic and Potential Energy • This animation neglects friction and air resistance until the bottom of the hill. • Friction is provided by the unpacked snow. • Mechanical energy loss (nonconservative force) • Negative work

Problem Solving Insights • Determine if non-conservative forces are included. • If yes: MEf = ME0 + Wnc • If no: MEf = ME0 • Eliminate pieces that are zero before solving • Key words: starts from rest (KE0 = 0), ends on the ground (PEf = 0), etc.

Example 1 • The Magnum XL-200 at Cedar Point includes a vertical drop of 59.4m. Assume the roller coaster has a speed of nearly zero at the crest of the hill. Neglecting friction, find the speed of the coaster at the bottom of the hill. MEf = ME0 KEf+ PEf = KE0 + PE0 ½ mvf2 + mghf= ½ mv02 + mgh0 ½ mvf2 = mgh0 (mass cancels!) vf2 = 2(9.8)(59.4) → vf= 34.1 m/s

Example 2 • A 55.0 kg skateboarder starts out with a speed of 1.80 m/s. He does +80.0J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. The final speed of the skateboarder is 6.00 m/s. • a) Calculate the change in gravitational potential energy. Solving for

Example 2 • A 55.0 kg skateboarder starts out with a speed of 1.80 m/s. He does +80.0J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. The final speed of the skateboarder is 6.00 m/s. • b) How much has the vertical height of the skater changed, and is the skater above or below the starting point? The skater is about 2 meters below the starting point.

Example 3 • A 2.00kg rock is released from rest from a height of 20.0 m. Ignore air resistance & determine the kinetic, potential, & mechanical energy at each of the following heights: 20.0 m, 12.0m, 0m (Round g to 10 m/s2 for ease)

Example 3 - Answers Start Here Then Use This

Example 4 Find the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations below. max Energy

Example 4 - Answers , so , so so at the top, so so

Unit 4 - Work and Energy