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

2024
Views:

279

Pages:

1
Author:

ui4s3l4md25

PROBLEM 3.84 Three workers trying to move a (3 \times 3 \times 4)-ft crate apply to the crate the three horizontal forces shown. (a) If (P = 60) lb, replace the three forces with an equivalent force-couple system at (A). (b) Replace the force-couple system of part (a) with a single force, and determine where it should be applied to side (AB). (c) Determine the magnitude of (P) so that the three forces can be replaced with a single equivalent force applied at 1 (B). SOLUTION (a) Based on [\Sigma F_x: -50~\text{lb} + 50~\text{lb} + 60~\text{lb} = F_A] [F_A = 60~\text{lb}] [\text{or } \mathbf{F}_A = (60.0~\text{lb})\mathbf{k}] Based on [\Sigma M_A: (50~\text{lb})(2~\text{ft}) - (50~\text{lb})(0.6~\text{ft}) = M_A] [M_A = 70~\text{lb-ft}] [\text{or } \mathbf{M}_A = (70.0~\text{lb-ft})\mathbf{j}] (b) Based on [\Sigma F_x: -50~\text{lb} + 50~\text{lb} + 60~\text{lb} = F] [F = 60~\text{lb}] [\text{or } \mathbf{F} = (60.0~\text{lb})\mathbf{k}] Based on [\Sigma M_A: 70~\text{lb-ft} = 60~\text{lb}(x)] [x = 1.16667~\text{ft}] [\text{or } x = 1.167~\text{ft} \text{ from } A \text{ along } AB] (c) Based on [\Sigma M_B: -(50~\text{lb})(1~\text{ft}) + (50~\text{lb})(2.4~\text{ft}) - P(3~\text{ft}) = R(0)] [P = \frac{70}{3} = 23.333~\text{lb}] [\text{or } P = 23.3~\text{lb}]