Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_11

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A former student of mechanics wishes to weigh himself but has access only to a scale A with capacity limited to 100 lb and a small 20-lb spring dynamometer B. With the rig shown he discovers that when he exerts a pull on the rope so that B registers 19 lb, the scale A reads 67 lb. What is his correct weight? Problem 3/11 (a) Determination of the man's correct weight 1. Formula: Based on the equilibrium of the man in the vertical direction, we sum the forces. The man is pulled upward by the rope he holds in his hands and by the tension in the pulley system attached to his harness. The scale provides an upward normal force. From the pulley diagram, the tension in the rope is . The number of rope segments supporting the lower pulley block (attached to the harness) is . Thus, the upward force on the harness is . The man pulls the rope with tension , so the rope pulls up on his hands with . 2. Substitution: Substitute the given values: Scale reading: Dynamometer reading (rope tension): 3. Calculation: Calculate the total upward pull from the rope system: Add the scale reaction force: 4. Result: F = ∑ y 0⟹N + A T + hands F − harness W=0 T=T B n=4 F = harness 4T TT = hands T W=N + A T+4T=N + A 5T N = A 67 lb T=19 lb W=67+5(19) 5×19=95 lb 67+95=162 lb W=162 lb ● Final Conclusion: The student's correct weight is . ✨ Final Answer Summary (a) The student's correct weight is . Mecademy AI Solution · ENGProblem 3/11 162 lb 162 lb