Force, Motion & Energy - Structure & Story Line
The Structure of FM&E
In broad terms, the FM&E course divides naturally into three parts, which form a clear sequence. Chapter 1 introduces balanced forces acting along a line. Specifically, weight, the elastic force, the magnetic force, and friction are studied quantitatively, and lead to a discussion of Newton's third law. In Chapter 2, pressure is introduced, and attention shifts to forces exerted by liquids and gases. Chapter 3 brings in vectors to represent noncollinear forces and culminates with qualitative experimentation on the effects of forces on moving objects.
Chapter 4 covers motion, primarily motion at constant speed. The chapter emphasizes that an object can move at constant speed even though forces are acting on it, provided that the net force is zero. From the motion of objects at constant speed, the program proceeds to the motion of waves in homogeneous media (Chapter 5). The relations among time, distance, and speed developed in Chapter 4 are now applied to both longitudinal and transverse waves.
Since thermal energy is used in this course as a measure for other forms of energy, a thorough introduction to thermal energy is provided in Chapter 6. In the process, specific heat and heat of fusion are introduced experimentally. Finally, in Chapter 7, concepts studied in the prior chapters—namely, forces, change in position, and motion at constant speed—lead to an understanding of potential energy, kinetic energy, and the law of conservation of energy.
In addition to this thematic progression, skills that are introduced at the beginning of the course are applied throughout. Key examples include the idea of proportionality, which is developed in Chapter 1, and the use of histograms as a way to summarize class data and reach conclusions.
The Story Line of FM&E
The following annotated table of contents best illustrates the story line:
1.2 Experiment: Weight and the Spring Scale 1.3 Hooke's Law: Proportionality
1.4 Experiment: The Magnetic Force
1.5 Experiment: Sliding Friction
1.6 Friction and Weight
1.7 Newton's Third Law
Although "force" is a common word, its use in science is specific and quantitative. This idea is made clear in the brief introduction and in Experiment 1.2, in which a spring is calibrated in arbitrary weight- units to motivate the introduction of the newton scale. Extension of the spring as a function of weight (Experiment 1.2) is used as an example of proportionality, a concept that recurs throughout the course (Section 1.3). Further development of this topic, as well as reinforcement of graphing skills, appears in Appendixes 1 and 2. Experiment 1.4, in which the magnetic force between two magnets is measured as a function of the separation between the closest poles, introduces the idea of dependence of a force on distance. In recognition of the prominent role that the force of friction plays in daily life, we show that friction does not act on an object at rest unless there is also another force acting on the object. Students investigate the minimum force needed to keep a body moving under a variety of conditions (Experiment 1.5). Taken together with Section 1.6, this experiment makes it evident that friction depends on weight, not weight per unit area, providing a transition to the next chapter. Finally, Newton's third law is discussed for static situations.
2.1 Weight and Mass
2.2 Experiment: Mass, Volume, and Density
2.3 Force and Pressure
2.4 Experiment: Another Type of Balance
2.5 Pressure in Liquids
2.6 The Buoyant Force
2.7 Experiment: Testing a Prediction
2.8 Atmospheric Pressure
Later in the course, both weight and mass will be needed, so we now introduce the proportionality constant (g) between them. Since mass, especially for liquids, is often expressed as a product of density and volume, we introduce this relationship here (Experiment 2.2) and use it extensively in the rest of the chapter, as well as in later chapters. Students often confuse force and pressure. This chapter provides them with the opportunity to work with both concepts (Experiment 2.4). We demonstrate the dependence of pressure on depth and the independence of pressure from direction in liquids (Section 2.5). We then use these ideas to derive the buoyant force (Section 2.6). Students then test the results experimentally (Experiment 2.7). In Section 2.8, pressure in liquids is compared with pressure in gases.
3.1 Representing Forces
3.2 Experiment: Combining Forces
3.3 The Net Force
3.4 Forces and Their Components
3.5 Experiment: Forces Acting on Moving Bodies
3.6 Forces and Motion: A Summary
Through experience, students know that the effect of a force depends on its strength and direction. Since restricting force to a single line is quite artificial, we introduce vectors to represent forces. The usefulness of this representation is made clear in Experiment 3.2, in which the students balance forces exerted by three spring scales in a plane. The relationship between the combination of two forces and a third force that balances them is discussed in Section 3.3. A common misconception is that bodies move in the direction of the force acting on them. Students find out that this is not the case by blowing in various directions on a moving, low-friction puck (Experiment 3.5). The chapter concludes with a review that includes the formulation of Newton's first law.
4.1 Introduction to Black Boxes
4.2 Experiment: The Motion Detector - Measuring Distance
4.3 Experiment: The Motion Detector - Motion Graphs
4.4 Distance, Time, and Average Speed
4.5 Experiment: Terminal Speed
4.6 Working with Distance, Time, and Constant Speed
The traditional way of teaching kinematics (displacement - velocity - acceleration) is difficult even for high-school students. We consider it inappropriate at the level of this course. Instead, we work extensively with distance, time, and speed in the context of real-life situations. Our preferred way of introducing motion is with a motion detector, having students do the moving to promote kinesthetic learning(Sections 4.2 and 4.3). Section 4.4 introduces constant speed as an average speed that is the same in all intervals. A coffee filter dropped over a motion detector provides an example in which balanced forces produce motion at constant speed (Experiment 4.5). Combining the idea of constant speed with the ideas of distance and time provides the tools for solving a variety of problems using common units for these quantities (Section 4.6).
5.1 Sound: Something Else that Moves
5.2 Visualizing Sound: Longitudinal Waves
5.3 Experiment: The Speed of Sound
5.4 Waves in Gases and Liquids
5.5 Experiment: Transverse Waves on a Coil Spring
5.6 Waves in Solids
5.7 Internet Activity: Locating an Earthquake
Waves are of fundamental importance in science and provide examples for a variety of motions at constant speed. Their motion is fundamentally different from the motion of material objects (Section 5.1). To visualize sound waves, we generate longitudinal waves on a coil spring (Section 5.2). The speed of sound is measured in an outdoor experiment using simple equipment (Experiment 5.3). The coil spring is used to introduce transverse waves (Section 5.5). The discussion of waves in solids (transverse and longitudinal) is then applied to earthquakes (Sections 5.6 and 5.7).
6.2 Experiment: Mixing Warm and Cool Water
6.3 A Unit of Energy: The Joule
6.4 Experiment: Cooling a Warm Solid in Cool Water
6.5 Specific Heats of Different Substances
6.6 Experiment: Melting Ice
6.7 Heat of Fusion and Heat of Vaporization
6.8 Experiment: Dissolving a Solid in Water
The usefulness of the idea of energy stems from the convertibility of energy into different forms. All forms of energy can be associated with a change in temperature. In this program, we define a change in some phenomenon as a change in energy when the original change is associated with a change in temperature. Experiment 6.2 helps to emphasize the difference between temperature and thermal energy. The results of the experiments are generalized in Sections 6.3 - 6.5, where specific heat is introduced. Melting ice in a calorimeter leads into the ideas of heat of fusion and heat of evaporation (Experiment 6.6 and Section 6.7).
7.1 Experiment: Heating Produced by a Slowly Falling Object
7.2 Gravitational Potential Energy
7.3 Elastic Potential Energy
7.4 Kinetic Energy
7.5 Kinetic Energy as a Function of Speed
7.6 Experiment: Free Fall
7.7 The Law of Conservation of Energy
Gravitational potential energy is introduced through the use of a slowly falling weight to raise the temperature of an aluminum cylinder. The dependence of the temperature rise on the weight of the falling body for a fixed distance is part of the experiment (Experiment 7.1); the dependence on the height is discussed in Section 7.2. The results are generalized in an end-of-chapter problem to show that the change in gravitational potential energy depends only on the change in height and not on the distance traveled along a slope. An experiment measuring changes in elastic potential energy is described in Section 7.3. The increase in temperature generated by stopping a wheel with a heavy rim is described in detail, leading to the definition of kinetic energy (Sections 7.4 and 7.5). Once both gravitational potential energy and kinetic energy have been defined, their conversion is studied in a free-fall experiment using the motion detector (Section 7.6). The chapter is summed up with a discussion of the law of conservation of energy.