Explanation Given information: Show the Equation of the Potential Energy of the particle as follows: U = 2 x 3 − 2 x 2 − 7 x + 10 (1) Here, x is the position of the particle in meters. Calculation: Find the equilibrium position of the particle using the relation: d U d x = 0 d d x ( 2 x 3 − 2 x 2 − 7 x + 10 ) = 0 6 x 2 − 4 x − 7 + 0 = 0 6 x 2 − 4 x − 7 = 0 Show the solution of the Equation ( a x 2 + b x + c = 0 ) as follows: x = − b ± b 2 − 4 a c 2 a (2) Substitute 6 for a, ( − 4 ) for b , and ( − 7 ) for c in Equation (2). x = − ( − 4 ) ± ( − 4 ) 2 − 4 × 6 × ( − 7 ) 2 × 6 = 4 ± 13.564 12 = 1.463 , − 0.797 Thus, the equilibrium points are x 1 = 1.463 and x 2 = − 0.797

Essential University Physics Volume 1, Loose Leaf Edition (4th Edition)

4th Edition

ISBN: 9780135264669

Author: Richard Wolfson

Publisher: PEARSON

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Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.

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Chapter 12, Problem 23E

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To find: the position of stable and unstable equilibrium of the particle.

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Chapter 12, Problem 22E

Chapter 12, Problem 24P

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Chapter 12 Solutions

Essential University Physics Volume 1, Loose Leaf Edition (4th Edition)

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 - Give an example of an object on which the net...Ch. 12 - Prob. 3FTD 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 - How does a heavy keel help keep a boat from...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. 11FTD 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. 23E 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 - Repeat Example 12.2, now assuming that the...Ch. 12 - You are headwaiter at a new restaurant, and your...Ch. 12 - Climbers attempting to cross a stream place a...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 - A 5.0-m-long ladder has mass 9.5 kg and is leaning...Ch. 12 - Prob. 42P 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 - Youre called to testify in a product liability...Ch. 12 - Youre designing a vacation cabin at a ski resort....Ch. 12 - Prob. 62P 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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