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; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd Edition)

3rd Edition

ISBN: 9780134197319

Author: Richard Wolfson

Publisher: PEARSON

See similar textbooks

Concept explainers

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.

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12, Problem 41P

Chapter 12, Problem 43P

Students have asked these similar questions

No chatgpt pls will upvote Already got wrong chatgpt answer

An electron and a proton are each accelerated through a potential difference of 21.0 million volts. Find the momentum (in MeV/c) and the kinetic energy (in MeV) of each, and compare with the results of using the classical formulas. Momentum (MeV/c) relativistic classical electron proton Kinetic Energy (MeV)

Four capacitors are connected as shown in the figure below. (Let C = 20.0 µF.) (a) Find the equivalent capacitance between points a and b. µF (b) Calculate the charge on each capacitor, taking ΔVab = 14.0 V. 20.0 µF capacitor µC 6.00 µF capacitor µC 3.00 µF capacitor µC capacitor C µC

Chapter 12 Solutions

Essential University Physics: Volume 1; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd 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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.