Chapter 2.3 Announcements: Homework 2.3: due Tuesday, Feb. 26, in class Exercises: 32, 33, 34, 36, 41 Problems: 8, 9, 10, 12, 13, 17 All grades will continue to be posted at: http://www.wfu.edu/~gutholdm/Physics110/phy110.htm Listed by last four digits of student ID Midterm 1: Thursday, Feb. 14 Material: Chapters 1 & 2.1, 2.2 Practice Midterm is posted on Web Bring a calculator Important equations will be given on exam (know how to use them)

energy, momentum & angular momentum Chapter 2.3 Conservation of energy, momentum & angular momentum Demos and Objects Concepts roller coaster pendulum mass on spring bobbing up and down bumper cars pirouettes spinning objects conservation of energy conservation of momentum conservation of angular momentum conserved quantities are treasures to physicists (and you, too).

Conservation of energy: For an isolated system (no work is done on the system): energy is conserved energy can not be destroyed or created, it is just transformed from one form into another. Types of energy: gravitational potential energy other potential energy (elastic, chemical, electric, magnetic, …) kinetic energy (energy of objects in motion) thermal energy (heat)

Kinetic energy: The energy of an object in motion We mainly consider kinetic energy and (gravitational) potential energy, and we ignore frictional losses (ignore heat). So, the conservation of energy becomes: Kinetic energy: The energy of an object in motion Gravitational potential energy: Energy of an object due to being higher than a reference height The hotter a system, the more thermal energy it has

When doing (positive) work on a system the energy of the system increases. The increased energy can manifest itself as potential energy, kinetic energy or heat. When doing work on a system, the system is not isolated any longer After the work has been done, the system may be considered isolated again. Energy and Work Energy: the capacity to make things happen Work: is the transference of energy

Conservation of Energy: Potential and Kinetic We are ignoring friction and drag For question 2: i-clicker-1; -2; -3 What is the total energy of the sledder (m = 50 kg) at the top of the hill? What is the 1) total energy, 2) gravitational potential energy and 3) the kinetic energy on top of the 15 m bump? Speed? What is the total energy, gravitational potential energy and the kinetic energy at the bottom of the hill? Speed? How much work was done on the sledder when he was pulled up the hill by his brother? 15,000 9, 800 7,350 2,450 1,650

Question: Michael Jordan does a vertical leap of 1.0 m and dunks successfully. What was his original take-off velocity?

Observations About Bumper Cars Moving or spinning cars tend to keep doing so It takes time to change a car’s motion Impacts change velocities & ang. velocities Cars often seem to exchange their motions Heavily loaded cars are hardest to redirect Heavily loaded cars pack the most wallop

Momentum = Mass · Velocity A translating bumper car carries momentum Momentum A conserved quantity (can’t create or destroy in an isolated system, no external force applied) A directed (vector) quantity Measures difficulty reaching velocity Momentum = Mass · Velocity

Conservation of momentum A man (m = 110 kg, including shoes) stands on a frozen pond with no friction and he wants to get to the shore, which is 100 m away. How can he accomplish that? i-clicker-4, question b) He takes off one of his boots (m = 10 kg) and throws it with a velocity of 10 m/s in the opposite direction of the shore. What’s his velocity (speed and direction)? How long will it take him to get to the shore? How do space ships move in empty space? - 0 - 1 m/s - 2 m/s - 5 m/s - 10 m/s

Exchanging Momentum  Impulse The only way to transfer momentum Impulse = Force · Time Impulse is a directed (vector) quantity Because of Newton’s third law: An impulse of one object on a second is accompanied by an equal but oppositely directed impulse of the second on the first.

Question: Why is it more painful to fall from a certain height on a hard floor than on a soft pile of leaves? After watching the Super Bowl you decide to play throw and catch with an egg. How do you have to catch it so that it does not break in your hands?

Momentum and impulse (change in momentum) A maiden is tied to the rails and you have to save her from a train (100,000 kg) which is approaching at a speed of 1 m/s. You gather all your strength (1000N) and stop the train just in time. What is the momentum of the train? How long did it actually take you to stop the train? Momentum is conserved. Where did it go?

Head-On Collisions Cars exchange momentum via impulse The least-massive car experiences largest change in velocity. The total momentum before and after a collision remains unchanged.

p1b Your small bumper car (m = 100 kg) has a velocity of 6 m/s and collides head-on with a large bumper car (m = 500 kg, at rest). It turns out that, after the collision, the large bumper car moves back with a velocity of v = 2 m/s. Before p1a p2a After v2 What is the total momentum of the two-car-system before the collision? What is it after the collision? What is the large car’s momentum after the collision? With what velocity to you move after the collision?

Angular Momentum A spinning object carries angular momentum A conserved quantity (can’t be created or destroyed in an isolated system) A directed (vector) quantity Measures difficulty reaching angular velocity Angular momentum = Moment of inertia · Angular velocity

Changing Moment of Inertia while spinning! For an isolated system (no torques applied): Angular momentum, L=I·w is constant!! Moment of inertia can change! An object that changes shape, also changes its moment of inertia. If I becomes smaller, w becomes larger (spins faster). Pirouettes: - Remember me rotating on platform - ice skaters doing pirouettes

i-clicker-5: You are riding on the edge of a spinning playground merry-go-round. If you walk towards the center of the merry-go-round, what will happen to its rotation? A. It will spin faster. B. It will spin slower. C. It will spin at the same rate.

i-clicker -6: You are standing still on a platform and hold a spinning bicycle wheel. You decide to flip the wheel. What will happen to you?? Nothing You start spinning in the wheels original direction The bicycle wheel stops spinning You start spinning opposite to the wheels original direction.

Why does a helicopter have two rotors??