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What happens when you are given a problem that is either too complex to solve or one where there are crucial ingredients missing? Many problems are very complex and cannot be solved if all the complexity is included.…
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Newton was certainly not the first person to see an apple fall from a tree. He may, however, have been the first to imagine the apple and the Moon to be one and the same. To Newton, the Moon was merely a much larger…
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This chapter focuses on finding the magnetic field. In the Biot-Savart law, the magnetic field is perpendicular to both the current element and the radiusvector. The magnetic field points out of the plane determined by…
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The analysis of the rolling wheel has become much simpler. The kinetic energy of the rolling wheel is equal to the rotational kinetic energy of the wheel about its center of mass plus the kinetic energy of the entire…
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Given a flashlight battery, a flashlight bulb, and a single piece of wire, hold them together to make the bulb light. Adults have taken more than an hour to light the bulb! And yet, this is the first activity in a…
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Visually, if not straight lines, then does nature favor curves? All curves are not equivalent. This chapter embarks on a brief tour of some simple physics with an eye toward the curves to discover along the way.
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Relativistic conservation laws
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Conservation laws are everywhere! Conservation of energy is one of the most useful laws in all branches of science. Other conservation laws in physics include charge, momentum, angular momentum, and those associated…
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How does a good theory get judged? It must first be able to explain what the prevailing theory has successfully explained. It must also be able to explain some known phenomenon that the prevailing theory is unable to…
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The search for the fundamental building blocks in nature has gone on for more than two thousand years. Aristotle felt that all the materials around us were composed of varying quantities of four basic elements—earth,…
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Sources, sinks, and gaussian spheres
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Conservation of mass requires that the flow of mass into the volume be equal to the flow of mass out of the volume. Another way of stating this is that the net flow of mass—or flux—through the surface must be zero. This…
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Archimedes’s law was a great achievement. Everybody knew that an object dropped in water made the water level rise (that is, it displaced some water). But Archimedes was the first to recognize that the amount of water…
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Up to now, all of the roller coasters of the world use a continuous track. But that does not restrict our imagination. In this chapter, we imagine that the top portion of the track is removed in a vertical loop,…
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Imagine paddling in a rowboat from one shore to the opposite shore with no current. The trip takes you 15 minutes. If you return to the river and venture across again, paddling to the opposite shore with the same…
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It Skips a Generation: Traits, Genes, and Crosses (Student Edition)
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Long before they understood why the strategy worked, farmers knew how to crossbreed plants to obtain more desirable traits. Even today, a farmer who knows nothing about genetics can tell you that when a blue type of…
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It Skips a Generation: Traits, Genes, and Crosses (Teacher Edition)
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Many of the early discoveries in genetics occured in plants. Plants have a few special characteristics that make them ideal for studying genetics. From one known cross, many genetically similar "siblings" are produced.…
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