Read and Analyze the sample problems given. Give a thorough analysis stating what type of situation the author dealt, how the problem was solved, the assumptions that the author considered in solving the problem, and why where these assumptions made. Sample Problem 7.7The spool in Fig. (a) weighs 25 N, and its center of gravity is located at the geo-metric center. The weight of block C is 50 N. The coefficients of static friction atthe two points of contact are as shown. Determine the largest horizontal force Pthat can be applied without disturbing the equilibrium of the system.ADimensions4, = 0.3in mm80120Hj = 0.4-B(a) SolutionThe key to the analysis of this problem is understanding that there are two possi-bilities for impending motion (both could occur simultaneously): (1) impendingsliding at A with impending rolling (without sliding) at B, and (2) impendingsliding at B with impending rolling (without sliding) at A. Because it is initiallynot known which of these possibilities represents the actual mode of impendingmotion, this is a Type III problem.The free-body diagrams for the block and the spool are shown in Fig. (b).50 NObserve that both friction forces have been shown in their correct directions. TheNeforce P tends to slide points A and B on the spool to the right. Therefore, bothfriction forces are shown acting to the left on the FBD of the spool.Inspecting the FBDS in Fig. (b), we conclude from EF, = 0 that NA = 50 Nand Ng = 75 N. At this stage three unknowns remain in the FBD of the spool: FA,FB, and P. Because only two equilibrium equations are left (E F, = 0 has alreadybeen used), the remainder of the solution depends on the assumption regardingimpending motion.FAAssume Impending Sliding at AThis assumption gives us the additional equation FA = 0.3NA = 0.3(50) = 15 N.The FBD of the spool then yieldsA80EMB = 0 3 FA(240) – P(40) = 025 N120which givesBP = 6FA = 6(15) = 90.0 NFBAssume Impending Sliding at BThis assumption gives Fg =0.4Ng = 0.4(75) = 30 N. From the FBD of the spool,(b)we now obtainEMA = 0 3 - FB (240) + P(200) = 0which givesP = 1.2FB = 1.2(30) = 36.0 NChoose the Correct AnswerUp to this point, the analysis has determined that sliding impends at A ifP=90.0 N and at B if P=36.0 N. Consequently, the largest force P that canbe applied without disturbing the static equilibrium of the spool isP = 36.0 NAnswerwith sliding impending at B.An alternate method for solving this problem is to assume impending slidingat one surface and then to compare the friction force at the other surface with itslimiting static value.

Sample Problem 7-7 The spool in Fig. (a) weighs 25 N, and its center of gravity is located at the geo- metric center. The weight of block C is 50 N. The coefficients of static friction at the two points of contact are as shown. Determine the largest horizontal force P that can be applied without disturbing the equilibrium of the system. A 4, = 0.3 Dimensions in mm 80 120 H, = 0.4 B

Sample Problem 7-7 The spool in Fig. (a) weighs 25 N, and its center of gravity is located at the geo- metric center. The weight of block C is 50 N. The coefficients of static friction at the two points of contact are as shown. Determine the largest horizontal force P that can be applied without disturbing the equilibrium of the system. A 4, = 0.3 Dimensions in mm 80 120 H, = 0.4 B

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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