Explanation Given information: The mass ( M ) of the ladder is 9.5 kg . Consider the mass of the person is m. The angle made by the ladder with the horizontal is 66 ° . The coefficient of friction ( μ ) between the ladder and the ground is 0.42 . The length ( L ) of the ladder is 5 m . Refer Appendix E. Take the value of gravitational acceleration as g = 9.8 m/s 2 . Calculation: Show the forces acting on the person as shown in Figure 1. Refer Figure 1. Consider the frictional force acting at the foot of the ladder is f , such that f = μ n 1 Here, n 1 is the normal reaction. Take the summation of the forces in the vertical direction and Equate to zero. ∑ F y = 0 n 1 − M g − m g = 0 n 1 = ( M + m ) g Consider the normal reaction at the wall is denoted by n w . Take the summation of the torque about the left end foot of the ladder and Equate to zero. ∑ τ = 0 n w L cos θ − M g × L 2 sin θ − m g ( α L sin θ ) n w L cos θ = m g ( α L sin θ ) + M g × L 2 sin θ Divide both side of the Equation by L cos θ . n w = m g α tan θ + M g 2 tan θ = ( m α + M 2 ) g tan θ Show the condition for no slip of person in the ladder as follows: f = n w μ n 1 = n w (1) Substitute ( m α + M 2 ) g tan θ for n w , ( M + m ) g for n 1 in Equation (1). μ ( M + m ) g = ( m α + M 2 ) g tan θ μ ( M + m ) = ( m α + M 2 ) tan θ μ M + μ m = m α tan θ + M tan θ 2 μ m − m α tan θ = M tan θ 2 − μ M m ( μ − α ( 1 cot θ ) ) = M ( 1 2 cot θ

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

4th Edition

ISBN: 9780135264669

Author: Richard Wolfson

Publisher: PEARSON

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Question

Chapter 12, Problem 42P

To determine

To find: the height on the ladder in Problem 41, climbed by the 95 kg person before the ladder start to slip.

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Chapter 12, Problem 41P

Chapter 12, Problem 43P

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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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