Meriam, Kraige & Bolton — Statics of Particles: Problem 2_23

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/23 It is desired to remove the spike from the timber by applying force along its horizontal axis. An obstruction A prevents direct access, so that two forces, one 400 lb and the other P, are applied by cables as shown. Compute the magnitude of P necessary to ensure a resultant T directed along the spike. Also find T. Problem 2/23 1. Analysis of Force Directions and Components To ensure the resultant force is directed along the horizontal axis of the spike, the net vertical component of the applied forces must be zero. We define a coordinate system with the -axis directed horizontally to the right and the -axis directed vertically upwards. For the 400-lb force (): The slope is defined by a horizontal run of 8" and a vertical drop of 6". The hypotenuse is ". For the unknown force : The slope is defined by a horizontal run of 8" and a vertical rise of 4". The hypotenuse is ". 2. Determination of Magnitude P ● Calculation Process 1. Present Final Formula: Since the resultant must be horizontal, the sum of vertical components must be zero: T xy F 1 L = 1 = 8+6 22 10 F = 1x 400 =( 10 8 )320 lb F = 1y −400 =( 10 6 )−240 lb P L = P = 8+4 22 = 80 4 5 P = x P = ( 80 8 )P = ( 4 5 8 ) 5 2P P = y P = ( 80 4 )P = ( 4 5 4 ) 5 P F = ∑ y 0⇒P + y F = 1y 0 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The magnitude of the force required to keep the resultant horizontal is approximately 537 lb. 3. Determinat