Explanation Given information: The weight of model of the earth, C is ( W ) is 12 lb. The radius of horizontal circle ( ρ ) is 3 ft. Calculation: Sketch the free body diagram and kinetic diagram of fly ball as shown in Figure (1). Consider along y -axis as positive. Apply Newton’s law of equation along y -axis. Σ F y = 0 T C A cos 40 ° − T C B cos 15 ° − W = 0 0.76604 T C A − 0.96593 T C B = W (1) Here, T C A is the tension in the wire DA and T C B is the tension in the wire CB . Substitute 12 lb for W in Equation (1). 0.76604 T C A − 0.96593 T C B = 12 (2) Find the equation of tension in the wire CB using Equation (2): 0.76604 T C A − 0.96593 T C B = 12 0.96593 T C B = 0.76604 T C A − 12 T C B = 0.79307 T C A − 12.423 (3) Find the equation of force in the link CA using Equation (2): 0.76604 T C A − 0.96593 T C B = 12 0.76604 T C A = 0.96593 T C B + 12 T C A = 1.26093 T C B + 15.665 (4) Consider along n -axis as positive. Apply Newton’s law of equation along n -axis. Σ F n = m a n T C A sin 40 ° + T C B sin 15 ° = m ( v 2 ρ ) Here, v is the velocity of model C . Substitute W g for m . T C A sin 40 ° + T C B sin 15 ° = ( W g ) v 2 ρ Substitute 12 lb for W , 32.2 ft/s 2 for g , 3 ft for ρ . T C A sin 40 ° + T C B sin 15 ° = ( 12 32.2 ) v 2 3 0.64279 T C A + 0.25882 T C B = 0.1242 v 2 v 2 = 5.1745 T C A + 2.084 T C B (5) The tension in the wires not exceeds 26 lb. Therefore, the tension in the wires can be calculated by trial and error method. Find the maximum force in the wires CB and CA. Assume the force in wire CB is 26 lb. Find the force in link CA using the Equation (4)

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Chapter 12.1, Problem 12.42P

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The range of the allowable values of v if both wires are to remain taut and if the tension in either of the wires is not to exceed 26 lb.

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Chapter 12.1, Problem 12.41P

Chapter 12.1, Problem 12.43P

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