Explanation Given information: The combined weight of the spool and the wire is W = 200 lb . The coefficient of static friction at A and B is μ s = 0.40 . The coefficient of kinetic friction at A and B is μ k = 0.30 . Calculation: Show the free-body diagram of the wire and spool as in Figure 1. Find the friction force ( F ) using the relation. F = μ k N Here, the coefficient of kinetic friction is μ k and the normal force is N . Find the total friction force at point A and B as follows; F A = μ k N A F B = μ k N B Take moment about point G . ∑ M G = 0 P ( 3 ) − F A ( 6 ) − F B ( 6 ) = 0 Substitute μ k N A for F A and μ k N B for F B . P ( 3 ) − μ k N A ( 6 ) − μ k N B ( 6 ) = 0 Substitute 0.30 for μ k . P ( 3 ) − 0.30 N A ( 6 ) − 0.30 N B ( 6 ) = 0 3 P − 1.8 N A − 1.8 N B = 0 P = 0.6 N A + 0.6 N B (1) Resolve the vertical component of forces. ↑ ∑ F y = 0 P + N A + F B − 20 = 0 Substitute μ k N B for F B . P + N A + μ k N B − 20 = 0 Substitute 0.30 for μ k . P + N A + 0

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 8.1, Problem 8.19P

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Chapter 8 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 8.1 - Knowing that the coefficient of friction between...Ch. 8.1 - Two blocks A and B are connected by a cable as...Ch. 8.1 - A cord is attached to and partially wound around a...Ch. 8.1 - A 40-kg packing crate must be moved to the left...Ch. 8.1 - Determine whether the block shown is in...Ch. 8.1 - Determine whether the block shown is in...Ch. 8.1 - Determine whether the block shown is in...Ch. 8.1 - Determine whether the block shown is in...Ch. 8.1 - Knowing that = 45 in Prob. 8.1, determine the...Ch. 8.1 - The 20-lb block A hangs from a cable as shown....

Ch. 8.1 - The 10-kg block is attached to link AB and rests...Ch. 8.1 - Considering only values of less than 90,...Ch. 8.1 - Prob. 8.9P Ch. 8.1 - Prob. 8.10P Ch. 8.1 - The 50-lb block A and the 25-lb block B are...Ch. 8.1 - The 50-lb block A and the 25-lb block B are...Ch. 8.1 - Three 4-kg packages A, B, and C are placed on a...Ch. 8.1 - Prob. 8.14P Ch. 8.1 - A uniform crate with a mass of 30 kg must be moved...Ch. 8.1 - A worker slowly moves a 50-kg crate to the left...Ch. 8.1 - Prob. 8.17P Ch. 8.1 - A 200-lb sliding door is mounted on a horizontal...Ch. 8.1 - Prob. 8.19P Ch. 8.1 - Prob. 8.20P Ch. 8.1 - Prob. 8.21P Ch. 8.1 - Prob. 8.22P Ch. 8.1 - The 10-lb uniform rod AB is held in the position...Ch. 8.1 - Prob. 8.24P Ch. 8.1 - Prob. 8.25P Ch. 8.1 - Prob. 8.26P Ch. 8.1 - The press shown is used to emboss a small seal at...Ch. 8.1 - The machine base shown has a mass of 75 kg and is...Ch. 8.1 - Prob. 8.29P Ch. 8.1 - Prob. 8.30P Ch. 8.1 - Prob. 8.31P Ch. 8.1 - Prob. 8.32P Ch. 8.1 - Prob. 8.33P Ch. 8.1 - A driver starts the engine of an automobile that...Ch. 8.1 - Prob. 8.35P Ch. 8.1 - Two uniform rods each of weight W and length L are...Ch. 8.1 - A 1.2-m plank with a mass of 3 kg rests on two...Ch. 8.1 - Two identical uniform boards, each with a weight...Ch. 8.1 - A uniform 20-kg tube resting on a loading dock...Ch. 8.1 - Prob. 8.40P Ch. 8.1 - A 10-ft beam, weighing 1200 lb, is to be moved to...Ch. 8.1 - (a) Show that the beam of Prob. 8.41 cannot be...Ch. 8.1 - Two 8-kg blocks A and B resting on shelves are...Ch. 8.1 - Prob. 8.44P Ch. 8.1 - Prob. 8.45P Ch. 8.1 - Two slender rods of negligible weight are...Ch. 8.1 - Two slender rods of negligible weight are...Ch. 8.2 - The machine part ABC is supported by a...Ch. 8.2 - Prob. 8.49P Ch. 8.2 - Prob. 8.50P Ch. 8.2 - Prob. 8.51P Ch. 8.2 - Prob. 8.52P Ch. 8.2 - Solve Prob. 8.52 assuming that the end of the beam...Ch. 8.2 - Prob. 8.54P Ch. 8.2 - Prob. 8.55P Ch. 8.2 - Block A supports a pipe column and rests as shown...Ch. 8.2 - A 200-lb block rests as shown on a wedge of...Ch. 8.2 - Prob. 8.58P Ch. 8.2 - Prob. 8.59P Ch. 8.2 - Prob. 8.60P Ch. 8.2 - Prob. 8.61P Ch. 8.2 - An 8 wedge is to be forced under a machine base at...Ch. 8.2 - Prob. 8.63P Ch. 8.2 - A 15 wedge is forced under a 50-kg pipe as shown....Ch. 8.2 - A 15 wedge is forced under a 50-kg pipe as shown....Ch. 8.2 - Prob. 8.66P Ch. 8.2 - Prob. 8.67P Ch. 8.2 - Prob. 8.68P Ch. 8.2 - Prob. 8.69P Ch. 8.2 - Prob. 8.70P Ch. 8.2 - Prob. 8.71P Ch. 8.2 - The position of the automobile jack shown is...Ch. 8.2 - Prob. 8.73P Ch. 8.2 - Prob. 8.74P Ch. 8.2 - In the vise shown, the screw is single-threaded in...Ch. 8.2 - Prob. 8.76P Ch. 8.3 - A lever of negligible weight is loosely fitted...Ch. 8.3 - Prob. 8.78P Ch. 8.3 - 8.79 and 8.80 The double pulley shown is attached...Ch. 8.3 - Prob. 8.80P Ch. 8.3 - 8.81 and 8.82 The double pulley shown is attached...Ch. 8.3 - Prob. 8.82P Ch. 8.3 - Prob. 8.83P Ch. 8.3 - The block and tackle shown are used to lower a...Ch. 8.3 - Prob. 8.85P Ch. 8.3 - Prob. 8.86P Ch. 8.3 - Prob. 8.87P Ch. 8.3 - 8.87 and 8.88 A lever AB of negligible weight is...Ch. 8.3 - Prob. 8.89P Ch. 8.3 - Prob. 8.90P Ch. 8.3 - Prob. 8.91P Ch. 8.3 - Prob. 8.92P Ch. 8.3 - Prob. 8.93P Ch. 8.3 - Prob. 8.94P Ch. 8.3 - Prob. 8.95P Ch. 8.3 - Prob. 8.96P Ch. 8.3 - Solve Prob. 8.93 assuming that the normal force...Ch. 8.3 - Prob. 8.98P Ch. 8.3 - Prob. 8.99P Ch. 8.3 - A 900-kg machine base is rolled along a concrete...Ch. 8.3 - Prob. 8.101P Ch. 8.3 - Prob. 8.102P Ch. 8.4 - A rope having a weight per unit length of 0.4...Ch. 8.4 - A hawser is wrapped two full turns around a...Ch. 8.4 - Two cylinders are connected by a rope that passes...Ch. 8.4 - Prob. 8.106P Ch. 8.4 - The coefficient of static friction between block B...Ch. 8.4 - Prob. 8.108P Ch. 8.4 - A band belt is used to control the speed of a...Ch. 8.4 - Prob. 8.110P Ch. 8.4 - The setup shown is used to measure the output of a...Ch. 8.4 - A flat belt is used to transmit a couple from drum...Ch. 8.4 - Prob. 8.113P Ch. 8.4 - Prob. 8.114P Ch. 8.4 - The speed of the brake drum shown is controlled by...Ch. 8.4 - The speed of the brake drum shown is controlled by...Ch. 8.4 - Prob. 8.117P Ch. 8.4 - Bucket A and block C are connected by a cable that...Ch. 8.4 - Prob. 8.119P Ch. 8.4 - Prob. 8.120P Ch. 8.4 - 8.121 and 8.123 A cable is placed around three...Ch. 8.4 - Prob. 8.122P Ch. 8.4 - Prob. 8.123P Ch. 8.4 - Prob. 8.124P Ch. 8.4 - Prob. 8.125P Ch. 8.4 - Prob. 8.126P Ch. 8.4 - The axle of the pulley is frozen and cannot rotate...Ch. 8.4 - The 10-lb bar AE is suspended by a cable that...Ch. 8.4 - Prob. 8.129P Ch. 8.4 - Prove that Eqs. (8.13) and (8.14) are valid for...Ch. 8.4 - Complete the derivation of Eq. (8.15), which...Ch. 8.4 - Prob. 8.132P Ch. 8.4 - Solve Prob. 8.113 assuming that the flat belt and...Ch. 8 - 8.134 and 8.135 The coefficients of friction are S...Ch. 8 - Prob. 8.135RP Ch. 8 - Prob. 8.136RP Ch. 8 - A slender rod with a length of L is lodged between...Ch. 8 - The hydraulic cylinder shown exerts a force of 3...Ch. 8 - Prob. 8.139RP Ch. 8 - Bar AB is attached to collars that can slide on...Ch. 8 - Two 10 wedges of negligible weight are used to...Ch. 8 - A 10 wedge is used to split a section of a log....Ch. 8 - Prob. 8.143RP Ch. 8 - A lever of negligible weight is loosely fitted...Ch. 8 - In the pivoted motor mount shown, the weight W of...

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Find the required magnitude of the force P .

Solution Summary: The author shows the free-body diagram of the wire and spool as in Figure 1. Find the friction force (F) using the relation.

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Find the required magnitude of the force P.

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Chapter 8 Solutions