Kinetic and Potential: Energy of Motion Work and Power: Waterwheel Collisions and Momentum: Bouncing Balls What a Drag

On the topic of energy related to motion, this summary lesson is intended to tie together the concepts introduced in the previous four lessons and show how the concepts are interconnected in everyday applications. A hands-on activity demonstrates this idea and reinforces students' math skills in calculating energy, momentum and frictional forces.

For safety, when designing recreation and transportation vehicles, engineers take into account all of the energy of motion concepts. An engineer designing a scooter cannot focus on one concept, such as momentum, and ignore the effects of friction, mechanical energy or work on the scooter. No one would want to ride a scooter that overcomes friction so well that is does not stop! Consumers benefit from engineers who have a superb understanding of potential energy, kinetic energy, work, power, momentum, collisions, friction and drag. aerodynamic collision energy friction Joule Newton power momentum Watt work mechanical energy, work and power, momentum, and friction After this lesson, students should be able to: 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. 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. 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 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. 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. 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. 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. 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. 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. Both energies are measured in Joules (J) and can be defined as: PE = mass x g x height and where g is gravity measured as 9.81 meters/sec2 (32.2 feet/sec2) at sea level. 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. 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. 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. 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? (Ouch!) Friction and drag could be used to slow you down until you could safely step off of the board. Drag could be maximized by facing your body forward and outstretching your arms (silly looking, but definitely not aerodynamic). If you were a little more daring and needed to stop faster, you could press down on the back of the skateboard so the lip would grind against the ground to take advantage of friction. The force of friction on an object moving on a flat surface is defined as: FF = μ × W where FF 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. μs and μk are used in the cases of static friction and kinetic friction. Work and power were also discussed in previous lessons. Work is defined as force acting over a distance, or: Work = force × distance and power is defined as work divided by time, or: Power = force × distance ÷ time In the case of the skateboard coming to a stop, friction and drag would be doing work to bring you to a stop. However, this is a special case because the frictional forces would be acting in a direction opposite to your motion. Normally the force and distance are going in the same direction which gives a positive value of work. Conversely, the value of work is negative for frictional forces. Energy is the capacity to do work (units = Joules). Energy that is composed of both potential energy and kinetic energy. The energy of position, or stored energy. The energy of motion. Work over a period of time (units = Watts). Mass in motion (units = kg-meter/sec). The amount of momentum in a system remains the same after a collision. A collision in which all of the momentum is conserved. For example, a ball that bounces back up to its original height. A collision in which the kinetic energy is not conserved. For example, a ball that only bounces partially to its original height. The force that resists the motion of two objects pressed against each other. The resistance against an object to start moving or sliding. The resistance against an object already moving or sliding. An experimentally determined value that helps determine the amount of friction experienced between two objects. The frictional force that a fluid exerts upon an object traveling though it. Ramp and Review Ramp and Review (High School Activity) Engineers learn these principles of physical science in order to design vehicles for recreation and transportation. From skateboards and scooters to roller coasters and light rail trains, engineers must understand these concepts to design for safety. You would not want a scooter with wheels that do not provide any friction, or climb on a roller coaster that does not have enough momentum to make it back to the start of the ride. On a larger scale, you would not want to be on a train that has too much momentum to stop, or in a car that does not provide an inelastic collision during an accident. You would not want to fly a plane that does not have enough power to take off on the runway, or creates too much drag and runs out of fuel. Much of our everyday lives and safety depends on engineers designing with an understanding of these energy of motion concepts. Matching: Create a list of all the equations used in this lesson. Randomly write the left sides of the equations on the left side of the board and the right sides of the equations on the right side of the board. As a class, have the students match the correct sides together. For example, Momentum mass × g × height Potential energy force × distance Vocabulary: Ask the students to write down the vocabulary words and definitions on a sheet of paper or in their science journals. Question/Answer: Have students answer the following questions to gauge their understanding of the lesson concepts. What is the relationship between potential and kinetic energy of a falling object? (Answer: The object's potential energy is converted into kinetic as it falls.) Does an object's momentum increase while falling? (Answer: Yes) What kind of friction does a falling object experience? (Answer: Drag) Discussion Question: Ask the students and discuss as a class how the waterwheel was an example activity that showed a combination of energy, work and power, momentum, and friction. Ask students to suggest another example from the previous energy of motion lessons and activities that also shows a combination of energy, work and power, momentum, and friction. (Example answer: In the Lesson 4 Introduction / Motivation section, bobsledders were cited as real-life example of minimizing friction and drag. While going down the track, bobsledders also convert potential energy into kinetic energy. They also gain momentum to carry them through the turns and must have a powerful start when pushing the sled to help decrease their time.) Pairs Check: Have students work in pairs to answer following questions. 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? (Answer: Mechanical energy = 4.824 Joules. Momentum = .6 kg-m/s. See work, below.) ME = PE + KE = (m × g × h) + (½ × m × V2) ME = (.2 kg × 9.81 m/s2× 2 m) + (½ × .2 kg × [3 m/s]2) ME = 3.924 J + .9 J ME = 4.824 Joules Momentum = m x V = .2 kg x 3 m/s = .6 kg-m/s 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? (Answer: Work = 133.4 Joules. Power = 44.47 Watts. See work, below.) Work = Force × distance = 66.7 N × 2 m = 133.4 Joules Power = Work ÷ time = 133.4 ÷ 3 = 44.47 Watts 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? (Answer: 133.4 Joules. See work, below.) PE = m × g × h = 6.8 kg × 9.81 m/s2× 2 m = 133.4 Joules 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? (Answer: It should.) 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? (Answer: 50 Newtons. See work, below.) FF = μ × W = .1 × 500 N = 50 Newtons Why is work done by friction considered to be negative? (Answer: Work is positive when the force and distance are in the same direction. With friction, the force is always in the opposite direction of motion, hence a negative value of work.) As an open-ended design activity, propose to the students that they have been contracted by an amusement park to design a new roller coaster. Have the students sketch their design and explain how they took mechanical energy, momentum, work and power, and friction into consideration. Remind the students that too much or too little of one thing may be disastrous. For example, too much friction, too little momentum, or too little potential energy in the beginning will cause the ride to stop in the middle of the track. However, too much momentum or kinetic energy might cause the ride to jump off of the track. Asimov, Isaac. The History of Physics. New York, NY: Walker & Co., 1984. Jones, Edwin R. and Richard L. Childers. Contemporary College Physics. Reading, MA: Addison-Wesley Publishing Co., 1993. Kahan, Peter. Science Explorer: Motion, Forces, and Energy. Upper Saddle River, NJ: Prentice Hall, 2000. Railroad Commission of Texas, Investigation Water Wheel activity: http://www.rrc.state.tx.us The Physics Classroom: Momentum and Its Conservation, at: http://www.physicsclassroom.com/Class/momentum/momtoc.html Waterwheel Factory, at: http://www.waterwheelfactory.com.