Meriam, Kraige & Bolton — Statics of Particles: Problem 2_32

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/32 A force F of magnitude 60 N is applied to the gear. Determine the moment of F about point O. Problem 2/32 The problem asks for the moment of a given force about the center of a gear. The moment can be calculated by finding the perpendicular distance from the center to the line of action of the force, or by resolving the force into components and summing their moments. 1. Identify Given Data and Geometric Relations Magnitude of force: Radius of the gear: The angle of the force F is specified as relative to the tangent at the point of application. In gear mechanics, this is known as the pressure angle. From the diagram, the force F is directed such that it creates a clockwise rotation about point . 2. Determine the Moment Arm or Force Components There are two primary ways to approach this: ● Method 1: Using the Tangential Component Resolve the force F into a tangential component () and a radial component (). 1. The tangential component is perpendicular to the radius and thus contributes to the moment: 2. The radial component passes through point and does not create any moment: 3. The moment arm for is the gear radius . F=60N r=100mm=0.1m 20 ∘ O F t F r F = t F⋅cos(20) ∘ O F = r F⋅sin(20) ∘ F t r ● Method 2: Using the Perpendicular Distance (Moment Arm) 1. The perpendicular distance from point to the line of action of F is: 2. The moment magnitude is then . 3. Calculation Process We will use the tangential component method: 1. S