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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
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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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 7.7 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 Dimensions 4, = 0.3 in mm 80 120 Hj = 0.4- B (a)
Transcribed Image Text: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 Dimensions 4, = 0.3 in mm 80 120 Hj = 0.4- B (a)
Solution The key to the analysis of this problem is understanding that there are two possi- bilities for impending motion (both could occur simultaneously): (1) impending sliding at A with impending rolling (without sliding) at B, and (2) impending sliding at B with impending rolling (without sliding) at A. Because it is initially not known which of these possibilities represents the actual mode of impending motion, this is a Type III problem. The free-body diagrams for the block and the spool are shown in Fig. (b). 50 N Observe that both friction forces have been shown in their correct directions. The Ne force P tends to slide points A and B on the spool to the right. Therefore, both friction 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 N and 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 already been used), the remainder of the solution depends on the assumption regarding impending motion. FA Assume Impending Sliding at A This assumption gives us the additional equation FA = 0.3NA = 0.3(50) = 15 N. The FBD of the spool then yields A 80 EMB = 0 3 FA(240) – P(40) = 0 25 N 120 which gives B P = 6FA = 6(15) = 90.0 N FB Assume Impending Sliding at B This assumption gives Fg =0.4Ng = 0.4(75) = 30 N. From the FBD of the spool, (b) we now obtain EMA = 0 3 - FB (240) + P(200) = 0 which gives P = 1.2FB = 1.2(30) = 36.0 N Choose the Correct Answer Up to this point, the analysis has determined that sliding impends at A if P=90.0 N and at B if P=36.0 N. Consequently, the largest force P that can be applied without disturbing the static equilibrium of the spool is P = 36.0 N Answer with sliding impending at B. An alternate method for solving this problem is to assume impending sliding at one surface and then to compare the friction force at the other surface with its limiting static value.
Transcribed Image Text:Solution The key to the analysis of this problem is understanding that there are two possi- bilities for impending motion (both could occur simultaneously): (1) impending sliding at A with impending rolling (without sliding) at B, and (2) impending sliding at B with impending rolling (without sliding) at A. Because it is initially not known which of these possibilities represents the actual mode of impending motion, this is a Type III problem. The free-body diagrams for the block and the spool are shown in Fig. (b). 50 N Observe that both friction forces have been shown in their correct directions. The Ne force P tends to slide points A and B on the spool to the right. Therefore, both friction 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 N and 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 already been used), the remainder of the solution depends on the assumption regarding impending motion. FA Assume Impending Sliding at A This assumption gives us the additional equation FA = 0.3NA = 0.3(50) = 15 N. The FBD of the spool then yields A 80 EMB = 0 3 FA(240) – P(40) = 0 25 N 120 which gives B P = 6FA = 6(15) = 90.0 N FB Assume Impending Sliding at B This assumption gives Fg =0.4Ng = 0.4(75) = 30 N. From the FBD of the spool, (b) we now obtain EMA = 0 3 - FB (240) + P(200) = 0 which gives P = 1.2FB = 1.2(30) = 36.0 N Choose the Correct Answer Up to this point, the analysis has determined that sliding impends at A if P=90.0 N and at B if P=36.0 N. Consequently, the largest force P that can be applied without disturbing the static equilibrium of the spool is P = 36.0 N Answer with sliding impending at B. An alternate method for solving this problem is to assume impending sliding at one surface and then to compare the friction force at the other surface with its limiting static value.
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