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Problem Set 4

# Problem Set 4 - Problem Set IV Assign Fall 2006 Physics...

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Problem Set IV- Assign Sep 27, 2006 Fall 2006 Physics 200a Figures at the end R. Shankar Many problems ask for answers in terms of symbols and not numbers. You may need to invoke things like g in the answer even if I did not explicitly define them. 1. (i) Using the dot product show that if A + B is perpendicular to A - B , then A = B .(ii) Use the dot product to relate vector components ( A x , A y ) in the standard frame to A 0 x , A 0 y ) measured in a frame rotated counterclockwise by an angle θ . Use the fact that components of a vector are just dot products with the corresponding basis vectors: A x = A · i etc. 2. If F ( x ) = Ax 3 / 2 find the work done by it in moving a body from x = 0 to x = A . 3. You have to choose between a 225-W fridge that costs \$ 1150 and a 425-W model that costs \$ 850. The first runs 11% of the time and the second runs 20% of the time. If electricity costs 9.5 cents/kWh when will you break even? (Use hours as the unit of time at first, go to days to report final answer.) 4. See the masses in Figure (1) which start out at rest. (i) Find the velocity of the 14

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Problem Set 4 - Problem Set IV Assign Fall 2006 Physics...

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