Grade: - Page 50

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Modeling musical chords using sine waves Here is what the layout should look like: Introduction: The Introduction of your exploration can be broken down into three essential parts - Rationale ＝ Sets the background of your exploration and gives an argument for the choice of your topic. Your Rationale tells why you chose so and so topic. Aim of the idea/topic ＝ This is where you define your investigation′s objective and tell what you wish to achieve with this idea. Plan of Action ＝ It would help if you outlined the areas of mathematics you will be covering in your investigation. Body of your Exploration ＝ Elaborate on the method you used for the exploration and justify why you chose to proceed with that particular method. Use relevant mathematical tools like labelled graphs, charts, etc., for your mathematical work and explain them in the context. Conclusion ＝ State your results relating them with the Aim said in the beginning. The significance and impact of these results should be highlighted, as well. In addition to these, briefly tell how the exploration was useful to you and all you have gained from it. Explain in detail.

Modeling musical chords using sine waves Here is what the layout should look like: Introduction: The Introduction of your exploration can be broken down into three essential parts - Rationale ＝ Sets the background of your exploration and gives an argument for the choice of your topic. Your Rationale tells why you chose so and so topic. Aim of the idea/topic ＝ This is where you define your investigation′s objective and tell what you wish to achieve with this idea. Plan of Action ＝ It would help if you outlined the areas of mathematics you will be covering in your investigation. Body of your Exploration ＝ Elaborate on the method you used for the exploration and justify why you chose to proceed with that particular method. Use relevant mathematical tools like labelled graphs, charts, etc., for your mathematical work and explain them in the context. Conclusion ＝ State your results relating them with the Aim said in the beginning. The significance and impact of these results should be highlighted, as well. In addition to these, briefly tell how the exploration was useful to you and all you have gained from it. Explain in detail.

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Two particles move perpendicular to each other until they collide. (See image) Particle 1 has mass m and momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p. Note: Magnitudes are not drawn to scale in any of the figures. Suppose that after the collision, the particles "trade" their momenta, as shown in the figure. That is, particle 1 now has magnitude of momentum p , and particle 2 has magnitude of momentum 2p; furthermore, each particle is now moving in the direction in which the other had been moving. How much kinetic energy, K_lost , is lost in the collision? Express your answer in terms of m and p. Consider an alternative situation: This time the particles collide completely inelastically. How much kinetic energy K_lost is lost in this case? Express your answer in terms of m and p.

Two particles move perpendicular to each other until they collide. (See image) Particle 1 has mass m and momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p. Note: Magnitudes are not drawn to scale in any of the figures. Suppose that after the collision, the particles "trade" their momenta, as shown in the figure. That is, particle 1 now has magnitude of momentum p , and particle 2 has magnitude of momentum 2p; furthermore, each particle is now moving in the direction in which the other had been moving. How much kinetic energy, K_lost , is lost in the collision? Express your answer in terms of m and p. Consider an alternative situation: This time the particles collide completely inelastically. How much kinetic energy K_lost is lost in this case? Express your answer in terms of m and p.

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