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Introduction to Vectors and Basic Mechanics Concepts

By the end of Week 1, you should: · Understand course logistics . Be familiar with SI and FPS units · Know how to round numbers to a given number of significant figures · Remember the prefixes (kilo, Mega, ... ) · Understand the difference between weight and mass · Understand the difference between vectors and scalars . Be able to add vectors graphically ("head to tail" method) · Be able to multiply a vector by a scalar · Be able to calculate vector's magnitude from its components · Know Sine and Cosine Laws, be able to apply them to vector addition · Know what a Cartesian coordinate system is . Be able to add and subtract vectors in Cartesian components Questions · Is -v3 a scalar? · Explain in words, in full sentences, how you can find the magnitude of a resultant vector R = ? + B + ?: o Which information about the vectors A, B and C will you collect? o What will you do with this information? o How will you find R = |R|? · Assume that you have one vector equation: R = A + B + C. How many scalar equations does this equation correspond to? Assume that these vectors are coplanar (they all are in the same plane). . We discussed that if R = A + B, then Rx = Ax + Bx, and Ry = Ay + By. What can you say about the signs of the components Ax, Bx, Ay, By? Can they be negative, or are they always positive? If they can be negative, give an example. If they are always positive, explain why it is so. . Explain, in full sentences, what a component of a vector is, and how to find it.