Student engineers learn to understand force and motion and how it is effected by slope, design and weight carried.

Principles of Macroeconomics 2e covers the scope and sequence of most introductory economics courses. The text includes many current examples, which are handled in a politically equitable way. The outcome is a balanced approach to the theory and application of economics concepts. The second edition has been thoroughly revised to increase clarity, update data and current event impacts, and incorporate the feedback from many reviewers and adopters.Changes made in Principles of Macroeconomics 2e are described in the preface and the transition guide to help instructors transition to the second edition.

In this Unit, you will learn about:How Individuals Make Choices Based on Their Budget ConstraintThe Production Possibilities Frontier and Social ChoicesConfronting Objections to the Economic Approach

By the end of this section, you will be able to:

Interpret production possibilities frontier graphs
Contrast a budget constraint and a production possibilities frontier
Explain the relationship between a production possibilities frontier and the law of diminishing returns
Contrast productive efficiency and allocative efficiency
Define comparative advantage

Students explore building a pyramid, learning about the simple machine called an inclined plane. They also learn about another simple machine, the screw, and how it is used as a lifting or fastening device. During a hands-on activity, students see how the angle of inclination and pull force can make it easier (or harder) to pull an object up an inclined plane.

This lab demonstrates Hooke's Law with the use of springs and masses. Students attempt to determine the proportionality constant, or k-value, for a spring. They do this by calculating the change in length of the spring as different masses are added to it. The concept of a spring's elastic limit is also introduced, and the students test to makes sure the spring's elastic limit has not been reached during their lab tests. After compiling their data, they attempt to find an average value of the spring's k-value by measuring the slopes between each of their data points. Then they apply what they've learned about springs to how engineers might use that knowledge in the design of a toy that enables kids to jump 2-3 feet in the air.

Students are introduced to the health risks caused by cooking and heating with inefficient cook stoves inside homes, a common practice in rural developing communities. Students simulate the cook stove scenario and use the engineering design process, including iterative trials, to increase warmth inside a building while reducing air quality problems. Students then collect and graph data, and analyze their findings.

Students overlay USGS topographic maps into Google Earth’s satellite imagery. By analyzing Denali, a mountain in Alaska, they discover how to use map scales as ratios to navigate maps, and use rates to make sense of contour lines and elevation changes in an integrated GIS software program. Students also problem solve to find potential pathways up a mountain by calculating gradients.

Students investigate the relationships between angles and side lengths in right triangles with the help of materials found in the classroom and a mobile device. Using all or part of a meter stick or dowel and text books or other supplies, students build right triangles and measure the angles using a clinometer application on an Android® (phone or tablet) or iOS® device (iPhone® or iPad®). Then they are challenged to create a triangle with a given side length and one angle. The electronic device is used to measure the accuracy of their constructions.

Students learn how to quickly and efficiently interpret graphs, which are used for everyday purposes as well as engineering analysis. Through a practice handout completed as a class and a worksheet completed in small groups, students gain familiarity in talking about and interpreting graphs. They use common graph terminology such as independent variable, dependent variable, linear data, linear relationship and rate of change. The equation for calculating slope is explained. The focus is on students becoming able to clearly describe linear relationships by using the language of slope and the rate of change between variables. At lesson end, students discuss the relationship between variables as presented by the visual representation of a graph. Then they independently complete a homework handout.

Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.

Students use inclined planes as they recreate the difficult task of raising a monolith of rock to build a pyramid. They compare the push and pull of different-sized blocks up an inclined plane, determine the angle of inclination, and learn the changes that happen when the angle is increased or decreased.