# p3 - 2 K&K Problem 1.15 3 K&K Problem 1.19 Denote...

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Physics 21 Problem Set 3 Harry Nelson due Monday, January 29, In Class Course Info: The reading this week will be: 1)Review pp. 11-19, 2)pp. 39-45 on Taylor Series, 3)p. 52-75. The material from Chapter 2 has a lot of ‘enrichment’ material on the discussion of Newton’s Laws and units. I won’t focus much on the general discussion of the Laws and units, and will proceed to working problems fairly quickly. Prof. Nelson’s oﬃce hours: Friday 2-2:50pm 5103 Broida, 4:10-5:30pm in Phelps 1508. Richard Eager’s oﬃce hours are Monday 2:00-3:00pm, Tuesday 11:00-12:00noon, and Thursday 11:00-12:00noon in Broida 1019 (The Physics Study Room). 1. Consider the function f ( x ): f ( x ) = 1 cos( bx ) (a) Symbolically expand f ( x ) to third order about the point x = a ; that is, symbolically ﬁnd the coeﬃcients labeled ‘ c ’ in the equation: f ( x ) c 0 + c 1 ( x - a ) + c 2 ( x - a ) 2 + c 3 ( x - a ) 3 (b) Numerically evaluate the c coeﬃcients for the case b = 1 / 6 and a = π . (c) Plot both the exact value of f ( x ) and the third-order approximation for 0 < x < π , using the coeﬃcients of the last part.
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Unformatted text preview: 2. K&K Problem 1.15. 3. K&K Problem 1.19. Denote the radius of the tire R , and put your answers in terms of V , R , t , and of course ˆ ı and ˆ . I suggest pursuing the velocity of the pebble ﬁrst, using the results of the last problem. Then, the position will be equal to the integral of the velocity, plus a constant vector c x ˆ ı + c y ˆ . Choose c x and c y so that the pebble is at the origin when t = 0. 4. K&K Problem 2.1. 5. K&K Problem 2.3. 6. K&K Problem 2.4. 7. K&K Problem 2.7. 8. K&K Problem 2.8. 9. K&K Problem 2.16. Please do this problem initially for arbitrary incline angle, θ . There are two ways to go about this problem. .. you can work in an accelerated frame (see p. 62, where the equation F apparent = F true-M ¨ R is a direct generalization of the answer from Problem 1.15(a)). Or, you can implement the constraint equation discussed on the top half of p. 74....
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