Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_97

⚡ Mecademy AIENG정역학 · ch3  Problem Statement Determine the force required to begin rolling the uniform cylinder of mass over the obstruction of height . Problem 3/97 (a) Force required to begin rolling ● Calculation Process 1. Present Final Formula: To determine the minimum force required to begin rolling the cylinder over the obstruction, we consider the equilibrium of moments about the contact point at the corner of the obstruction, which we will call point . At the instant rolling begins, the cylinder just lifts off the floor, meaning the normal reaction force from the floor becomes zero. The condition for the start of rolling is: Let be the radius of the cylinder and be the height of the obstruction. The lever arms for the applied force and the weight about point are required. 2. Substitute Values: From the geometry of the system: The horizontal distance from the center of the cylinder to point (lever arm for the weight) is . The vertical distance from the center of the cylinder to point (lever arm for the force ) is . Substituting these into the moment equilibrium equation : 3. Partial Operations: Simplify the expression for the horizontal lever arm : Pm h P P A M = ∑ A 0 rh PW=mgA A d = w r−(r−h) 22 A Pd = P r−h ↺M =∑ A 0 P⋅(r−h)−mg⋅ = r−(r−h) 22 0 d w d = w r−(r−2rh+h) 222 d = w = 2rh−h 2 h(2r−h) Now substitute back into the equilibrium equation: 4. Final Calculation: Solve for : ● Final Conclusion: The horizontal force required to begin rolling the cylinder over the