University:
Angelo State University
Course:
ENGR 2301 | Engineering Mechanics - Statics
Academic year:

2024
Views:

116

Pages:

1
Author:

Ean Mason

PROBLEM 3.49 To lift a heavy crate, a man uses a block and tackle attached to the bottom of an I-beam at hook B. Knowing that the moments about the y and 1 z axes of the force exerted at B by portion AB of the rope are, respectively, 100 lb-ft and -400 lb-ft, determine the distance 2 a. SOLUTION diagram showing a block and tackle system with an Ibeam, hook B, and vectors T_BA, r_BA, M_O, and M_y Based on M_O = r_BA x T_BA where M_O = M_xi + M_yj + M_zk = M_xi + (100 lb-ft)j + (-400 lb-ft)k r_BA = (6 ft)i + (4 ft)j T_BA = λ_BAT_BA = [(6 ft)i - (12 ft)j - (a ft)k] / d_BA M_O = M_xi + 100j - 400k = |i j k| / d_BA * T_BA 6 4 0 6 -12 -a = (T_BA/d_BA)[-(4a)i + (6a)j - (96)k] From j-coefficient: 100d_BA = 6aT_BA or T_BA = 100d_BA / 6a (1) From k-coefficient: -400d_BA = -96T_BA or T_BA = 400d_BA / 96 (2) Equating Equations (1) and (2) yields 100(96) / 6(400) = a or a = 4.00 ft