Explanation Given information : The tension developed by a cord is 400 N. Draw the free body diagram of the forces acting in the cord DEF as shown below in Figure 1. Draw the free body diagram of the forces acting in the cord ABCD as in Figure 2. Determine tension in each cord by applying the Equation of equilibrium. At joint D . Along the vertical direction : ∑ F y = 0 F D E sin θ D E − W = 0 F D E = W sin θ D E (I) Here, the force acting on cord DE is F D E , the angle of cord DE is θ D E , and weight of the lamp is W . Along the horizontal direction : ∑ F x = 0 F D E cos θ D E − F C D = 0 F C D = F D E cos θ D E (II) Here, the force acting on cord CD is F C D . At joint D . Along the horizontal direction : ∑ F x = 0 F C D − F C A cos θ C A − F C B cos θ C B = 0 (III) Here, the force acting on cord CA is F C A , the angle of cord CA is θ C A , the force acting on cord CB is F C B , and the angle of cord CB is θ C B . Along the vertical direction : ∑ F y = 0 F C A sin θ C A − F C B sin θ C B = 0 (IV) Determine the mass of the lamp. W = m g (V) Here, the greatest tensile force is F and the acceleration due to gravity is g . Conclusion : Substitute 30 ° for θ D E in Equation (I). F D E = W sin 30 ° = 2 W Substitute 30 ° for θ D E and 2 W for F D E in Equation (II). F C D = 2 W × cos 30 ° = 1.732 W Substitute 1.732 W for F C D , ( 3 5 ) for cos θ C A , and 45 ° for θ C B in Equation (IV)

Engineering Mechanics: Statics & Dynamics, Student Value Edition Plus Modified Mastering Engineering Revision with Pearson eText -- Access Card Package

14th Edition

ISBN: 9780135841532

Author: HIBBELER, Russell , HIBBLER

Publisher: PEARSON

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Chapter 3.3, Problem 30P

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The maximum mass of the lamp.

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Engineering Mechanics: Statics & Dynamics, Student Value Edition Plus Modified Mastering Engineering Revision with Pearson eText -- Access Card Package

Ch. 3.3 - In each case, draw a free-body diagram of the ring...Ch. 3.3 - Write the two equations of equilibrium, Fx = 0 and...Ch. 3.3 - The crate has a weight of 550 lb. Determine the...Ch. 3.3 - The beam has a weight of 700 lb. Determine the...Ch. 3.3 - If the 5-kg block is suspended from the pulley B...Ch. 3.3 - The block has a mass of 5 kg and rests on the...Ch. 3.3 - If the mass of cylinder C is 40 kg, determine the...Ch. 3.3 - Determine the tension in cables AB, BC, and CD,...Ch. 3.3 - The members of a truss are pin connected at joint...Ch. 3.3 - The members of a truss are pin connected at joint...

Ch. 3.3 - Determine the magnitude and direction of F so...Ch. 3.3 - The bearing consists of rollers, symmetrically...Ch. 3.3 - The members of a truss are connected to the gusset...Ch. 3.3 - The gusset plate is subjected to the forces of...Ch. 3.3 - The man attempts to pull down the tree using the...Ch. 3.3 - The cords ABC and BD can each support a maximum...Ch. 3.3 - Determine the maximum force F that can be...Ch. 3.3 - The block has a weight of 20 lb and is being...Ch. 3.3 - Determine the maximum weight W of the block that...Ch. 3.3 - The lift sling is used to hoist a container having...Ch. 3.3 - A nuclear-reactor vessel has a weight of 500(103)...Ch. 3.3 - Determine the stretch in each spring for...Ch. 3.3 - The unstretched length of spring AB is 3 m. If the...Ch. 3.3 - Determine the mass of each of the two cylinders if...Ch. 3.3 - Determine the stiffness kT of the single spring...Ch. 3.3 - If the spring DB has an unstretched length of 2 m....Ch. 3.3 - Determine the unstretched length of DB to hold the...Ch. 3.3 - A vertical force P = 10 lb is applied to the ends...Ch. 3.3 - Determine the unstretched length of spring AC if a...Ch. 3.3 - The springs BA and BC each have a stiffness of 500...Ch. 3.3 - The springs BA and BC each nave a stiffness of 500...Ch. 3.3 - Determine the distances x and y for equilibrium if...Ch. 3.3 - Determine the magnitude of F1 and the distance y...Ch. 3.3 - The 30-kg pipe is supported at A by a system of...Ch. 3.3 - Each cord can sustain a maximum tension of 500 N....Ch. 3.3 - The streetlights A and B are suspended from the...Ch. 3.3 - Determine the tension developed in each cord...Ch. 3.3 - Prob. 30P Ch. 3.3 - Prob. 31P Ch. 3.3 - Prob. 32P Ch. 3.3 - The lamp has a weight of 15 lb and is supported by...Ch. 3.3 - Each cord can sustain a maximum tension of 20 lb....Ch. 3.3 - Prob. 35P Ch. 3.3 - Prob. 36P Ch. 3.3 - Prob. 37P Ch. 3.3 - Prob. 38P Ch. 3.3 - The ball D has a mass of 20 kg. If a force of F =...Ch. 3.3 - The 200-lb uniform container is suspended by means...Ch. 3.3 - The single elastic cord ABC is used to support the...Ch. 3.3 - A scale is constructed with a 4-ft-long cord and...Ch. 3.3 - The concrete wall panel is hoisted into position...Ch. 3.3 - Prob. 2CP Ch. 3.3 - Prob. 3CP Ch. 3.3 - Prob. 4CP Ch. 3.4 - Determine the magnitude of forces F1, F2, F3, so...Ch. 3.4 - Determine the tension developed in cables AB, AC,...Ch. 3.4 - Prob. 9FP Ch. 3.4 - Prob. 10FP Ch. 3.4 - Prob. 11FP Ch. 3.4 - The three cables are used to support the 40-kg...Ch. 3.4 - Determine the magnitudes of F1, F2, and F3 for...Ch. 3.4 - If the bucket and its contents have a total weight...Ch. 3.4 - Determine the stretch in each of die two springs...Ch. 3.4 - Prob. 47P Ch. 3.4 - Determine the tension in the cables in order to...Ch. 3.4 - Determine the maximum mass of the crate so that...Ch. 3.4 - Determine the force in each cable if F = 500 lb.Ch. 3.4 - Prob. 51P Ch. 3.4 - Determine the tens on developed in cables AB and...Ch. 3.4 - If the tension developed in each cable cannot...Ch. 3.4 - Prob. 54P Ch. 3.4 - Determine the maximum weight of the crate that can...Ch. 3.4 - The 25 kg flowerpot is supported at A by the three...Ch. 3.4 - If each cord can sustain a maximum tension of 50 N...Ch. 3.4 - Determine the tension developed m the three cables...Ch. 3.4 - Determine the tension developed in the three...Ch. 3.4 - Prob. 60P Ch. 3.4 - Prob. 61P Ch. 3.4 - If the maximum force in each rod con not exceed...Ch. 3.4 - Prob. 63P Ch. 3.4 - If cable AD is tightened by a turnbuckle and...Ch. 3.4 - Prob. 65P Ch. 3.4 - Prob. 66P Ch. 3.4 - Determine the maximum weight of the crate so that...Ch. 3.4 - The pipe is held in place by the vise. If the bolt...Ch. 3.4 - Prob. 2RP Ch. 3.4 - Prob. 3RP Ch. 3.4 - Prob. 4RP Ch. 3.4 - Prob. 5RP Ch. 3.4 - Prob. 6RP Ch. 3.4 - Determine the force in each cable needed to...Ch. 3.4 - If cable AB is subjected to a tension of 700 N,...

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The maximum mass of the lamp.

Solution Summary: The author explains how to determine the maximum mass of a lamp by drawing the free body diagram of the forces acting in the cord DEF as shown in Figure 1.

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