Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_24

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A bicyclist applies a 40-N force to the brake lever of her bicycle as shown. Determine the corresponding tension transmitted to the brake cable. Neglect friction at the pivot . Problem 3/24 (a) Determination of Tension ● Calculation Process 1. Present Final Formula: To find the tension in the cable, we apply the principle of moments about the pivot point . For equilibrium, the sum of moments must be zero: Taking counter-clockwise moments as positive: where is the applied force, is its perpendicular distance from , is the cable tension, and is its perpendicular distance from . 2. Substitute Values: From the diagram: Applied Force, Moment arm for , Moment arm for Tension , Substituting into the equilibrium equation: 3. Partial Operations: Calculate the moment generated by the applied force: Set up the equation for : TO T O M = ∑ O 0 T⋅d − T F⋅d = F 0 Fd F OT d T O F=40 N Fd = F 88 mm Td = T 22 mm T⋅(22 mm)−(40 N)⋅(88 mm)=0 M = F 40⋅88=3520 N⋅mm T 22⋅T=3520 4. Final Calculation: Solve for : ● Final Conclusion: The tension transmitted to the brake cable is . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 3/24 T T= 22 3520 T=160 N T160 N T=160 N