1. Lesson: Puttin' It All Together Contributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado at Boulder

2. Keywords: aerodynamic, collisio n, energy, friction, Jo ule, Newton, power, momentum, Watt, wo rk aerodynamiccollisio nenergyfrictionJo uleNewtonpower momentumWattwo rk

3. Learning Objectives Explain the concepts of kinetic and potential energy. Understand that energy can change from one form into another. Explain the difference between the scientific concepts of power and work.

4. Recognize the different types of friction: static friction, kinetic friction and drag. Understand that energy, momentum, power and work and friction can be described by equations

5. Calculate the amount of mechanical energy, momentum, power and work and friction in a system. Understand why energy of motion concepts are so fundamental to engineering design

6. Introduction The previous lessons and activities in this unit provided examples that demonstrate the physical science concepts of mechanical energy, work and power, momentum and collisions, and friction and drag.

7. While waterwheels were used as a demonstration of work and power, if you look deeper into a waterwheel system, you will see aspects of mechanical energy, momentum, and friction as well. Water turns the wheel by going from a high potential energy to kinetic energy.

8. Also, if there were no load on the waterwheel and the water supply ran out, the wheel would keep turning, showing signs of momentum. However, friction would eventually bring the wheel to a stop.

9. It is important to note that in real- world physical systems, these energy of motion concepts are commonly interconnected with each other. Much of our everyday lives and safety depend on engineers designing vehicles and structures with a firm understanding of these concepts and their interaction.

10. For example, skateboards, scooters, roller coasters, trains, cars, planes, trucks, elevators, etc. In this lesson, we put all of these concepts together to understand how they work collectively in a hands-on, inclined ramp activity.

11. Pre-Lesson Assessment Matching: Take out a sheet of paper. Use the box on the right side and left side of the board to make complete equations. There should be 6 total equations.

12. What is the relationship between potential and kinetic energy of a falling object? Does an object's momentum increase while falling? What kind of friction does a falling object experience?

13. Lesson In preceding lessons, we defined two types of mechanical energy: potential energy and kinetic energy. The potential energy of an object is based on position or height whereas the kinetic energy of an object is based on motion or velocity.

14. Both energies are measured in Joules (J) and can be defined as: PE = mass x g x height where g is gravity measured as 9.81 meters/sec 2 (32.2 feet/sec 2 ) at sea level. Energy

15. Kinetic Energy

16. Momentum As an object goes from a high to a low position or height, its potential energy is converted into kinetic energy. Naturally, as kinetic energy increases, the objects velocity increases and the object gains momentum.

17. Momentum is defined as: Momentum = mass x velocity with units measured in kg-meter/sec. With momentum, two types of collisions exist: elastic collisions, in which momentum is conserved, and inelastic collisions, in which momentum is not conserved.

18. A rubber ball and a ball of silly putty are good examples of objects that experience elastic and inelastic collisions. A rubber ball experiences elastic collisions and the silly putty experiences inelastic collisions.

19. Imagine you are on a skateboard, coming down a steep hill. You are converting your potential energy into kinetic while gaining momentum. How might you slow down and safely come to a stop without having an inelastic collision with the ground?

20. F F = μ x W A common equation used to determine the amount of friction an object experiences on a flat surface is: F F = μ x W where F F is the force of friction measured in Newtons (N) or pounds (lbs), μ is the coefficient of friction which is unit-less, and W is the weight of the object.

21. Work Work is defined as force acting over a distance, or: Work = force × distance

22. Power Power is defined as work divided by time, or: Power = force × distance ÷ time

23. Lesson Summary Assessment If a.2 kg Frisbee is 2 meters off the ground and flying at 3 meters/sec, how much total mechanical energy and momentum does it have?

24. If it took 66.7 Newtons of force to pick up your cat and place him on a ledge 2 meters high in 3 seconds, how much work did you do? How much power did you have?

25. If your cat weighs 66.7 Newtons (or 15 pounds) he has a mass of 6.8 kg. How much potential energy does your cat now have at 2 meters high?

26. Does it make sense that if you exert 133.4 Joules of work to lift your cat 2 meters, that she now has 133.4 Joules of potential energy?

27. If you weigh 500 Newtons and are sliding on ice, which has a coefficient of friction of.1 (μ), how much frictional force do your feet feel?