To determine The location and stability of equilibrium points with a = − 8 aJ / nm 2 and b = 1 aJ / nm 4 . Explanation Refer Example 12.4. Write the potential energy function. U ( x ) = a x 2 − b x 4 Differentiate the above equation with respect to x to find the points of equilibrium. d U ( x ) d x = d ( a x 2 − b x 4 ) d x = 2 a x − 4 b x 3 = 2 x ( a − 2 b x 2 ) (I) Equate d U ( x ) d x to zero. 2 x ( a − 2 b x 2 ) = 0 Solution of above equation gives the equilibrium points. Write the solution of above equation. x = 0 x = ± a 2 b Conclusion: Consider the case when x = 0 . The equilibrium point x = 0 is a point of local minimum in the potential energy curve. It means that x = 0 is a metastable point. Consider the case when x = ± a 2 b . To find the type of equilibrium point, find the second derivative of potential energy function. Differentiate equation (I) with respect to x again. d 2 U ( x ) d x 2 = d ( 2 a x − 4 b x 3 ) d x = 2 a − 12 b x 2 Rewrite the above expression by substituting ± a 2 b for x

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Chapter 12, Problem 26E

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The location and stability of equilibrium points with a=−8 aJ/nm2 and b=1 aJ/nm4.

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Chapter 12, Problem 24E

Chapter 12, Problem 27E

Chapter 12 Solutions

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Ch. 12.1 - The figure shows three pairs of forces acting on...Ch. 12.2 - Prob. 12.2GI Ch. 12.3 - The figure shows a person in static equilibrium...Ch. 12.4 - Prob. 12.4GI Ch. 12 - Give an example of an object on which the net...Ch. 12 - Prob. 2FTD Ch. 12 - Pregnant women often assume a posture with their...Ch. 12 - When you carry a bucket of water with one hand,...Ch. 12 - Is a ladder more likely to slip when you stand...Ch. 12 - Does choosing a pivot point in an equilibrium...

Ch. 12 - If you take the pivot point at the application...Ch. 12 - A short dog and a tall person are standing on a...Ch. 12 - Prob. 9FTD Ch. 12 - A body is subject to three forces; F1=1i+2jN,...Ch. 12 - To demonstrate that the choice of pivot point...Ch. 12 - In Fig. 12.11 the forces shown all have the same...Ch. 12 - Figure 12.12a shows a thin, uniform square plate...Ch. 12 - Repeat the preceding problem for the equilateral...Ch. 12 - A 23-m-long log of irregular cross section lies...Ch. 12 - A 60-kg uniform board 2.4 m long is supported by a...Ch. 12 - Where should the child in Fig. 12.14 sit if the...Ch. 12 - A 4.2-m-long beam is supported by a cable at its...Ch. 12 - Figure 12.15 shows how a scale with a capacity of...Ch. 12 - A portion of a roller-coaster track is described...Ch. 12 - Prob. 21E Ch. 12 - Prob. 22E Ch. 12 - Prob. 23E Ch. 12 - Example 12.2: Climbers attempting to cross a...Ch. 12 - Example 12.4: Consider the potential-energy curve...Ch. 12 - Prob. 27E Ch. 12 - Prob. 28E Ch. 12 - Youre a highway safety engineer, and youre asked...Ch. 12 - Figure 12.17a shows an outstretched arm with mass...Ch. 12 - A uniform sphere of radius R is supported by a...Ch. 12 - You work for a garden equipment company, and youre...Ch. 12 - Figure 12.20 shows the fool and lower leg of a...Ch. 12 - A uniform 5.0-kg ladder is leaning against a...Ch. 12 - The boom in the crane of Fig. 12.21 is free to...Ch. 12 - A uniform board of length L and weight W is...Ch. 12 - Figure 12.23 shows a 1250-kg car that has slipped...Ch. 12 - You are headwaiter at a new restaurant, and your...Ch. 12 - You are headwaiter at a new restaurant, and your...Ch. 12 - Prob. 41P Ch. 12 - A crane in a marble quarry is mounted on the...Ch. 12 - A rectangular block measures w w L, where L is...Ch. 12 - The potential energy as a function of position for...Ch. 12 - A rectangular block of mass m measures w w L,...Ch. 12 - A 160-kg highway sign of uniform density is 2.3 m...Ch. 12 - Prob. 47P Ch. 12 - Prob. 48P Ch. 12 - A uniform, solid cube of mass m and side s is in...Ch. 12 - An isosceles triangular block of mass m and height...Ch. 12 - Youre investigating ladder safety for the Consumer...Ch. 12 - A 2.0-m-long rod has density in kilograms per...Ch. 12 - What horizontal force applied at its highest point...Ch. 12 - A rectangular block twice as high as it is wide is...Ch. 12 - What condition on the coefficient of friction in...Ch. 12 - A uniform solid cone of height h and base diameter...Ch. 12 - Prove the statement in Section 12.1 that the...Ch. 12 - Three identical books of length L are stacked over...Ch. 12 - A uniform pole of mass M is at rest on an incline...Ch. 12 - For what angle does the situation in Problem 53...Ch. 12 - Figure 12.31 shows a popular system for mounting...Ch. 12 - The nuchal ligament is a thick, cordlike structure...Ch. 12 - A 4.2-kg plant hangs from the bracket shown in...Ch. 12 - The wheel in Fig. 12.34 has mass M and is weighted...Ch. 12 - An interstellar spacecraft from an advanced...Ch. 12 - Prob. 66P Ch. 12 - Engineers designing a new semiconductor device...Ch. 12 - Youve been hired by your states environmental...Ch. 12 - Youve been hired by your states environmental...Ch. 12 - Youve been hired by your states environmental...Ch. 12 - Youve been hired by your states environmental...

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