Implicit differentiation Given the following

Classical Mechanics 0
In Chapter 4 (at the end of Section 4.7) I claimed that, for a system with one degree of freedom, positions of stable equilibrium "normally" correspond to minima of the potential energy U (q). Using Lagrangian mechanics, you can now prove this claim. (a) Consider a one-degree system of N particles wi

Sears and Zemansky's University Physics with Modern Physics 13
Problem 7DQ Lane dividers on highways sometimes have regularly spaced ridges or ripples. When the tires of a moving car roll along such a divider, a musical note is produced. Why? Explain how this phenomenon could be used to measure the cars speed.

Physics for Scientists & Engineers with Modern Physics 4
Consider a straight section of wire of length d, as in Fig. 28-48, which carries a current I. (a) Show that the magnetic field at a point P a distance R from the wire along its perpendicular bisector is B = Mo I d 2ttR [d2 + 4R 2)\ (b) Show that this is consistent with Example 28-11 for an infinite w

Principles of Microeconomics 7
Suppose the book-printing industry is competitive and begins in a long-run equilibrium.a.Draw a diagram showing the average total cost, marginal cost, marginal revenue, and supply curve of the typical firm in the industry.b.Hi-Tech Printing Company invents a new process that sharply reduces the cost

Biology 8
Aquaporins exclude passage of hydronium ions (H30+). But recent research has revealed a role for some aquaporins in fat metabolism, in which they allow passage of glycerol, a three-carbon alcohol (see Figure 5.11), as well as H20. Since H30+ is much closer in size to water than is glycerol, what do y

Principles of Economics 6
The New York Times reported (Feb. 17, 1996) that subway ridership declined after a fare increase: There were nearly four million fewer riders in December 1995, the first full month after the price of a token increased 25 cents to $1.50, than in the previous December, a 4.3 percent decline. a. Use the

Psychology 5
According to Maslow, our most basic needs are a. self-actualization and self-esteem. b. shared with other animals. c. not experienced until higher needs are met. d. belongingness and love.

Principles of Economics 9
According to the theory of liquidity preference, an economys interest rate adjusts a. to balance the supply and demand for loanable funds. b. to balance the supply and demand for money. c. one-for-one to changes in expected inflation. d. to equal the interest rate prevailing in world financial market