Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_119

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Calculate the torque M which the engine of the pickup truck must supply to the rear axle to roll the front wheels over the curbing from a rest position if the rear wheels do not slip. Determine the minimum effective coefficient of friction at the rear wheels to prevent slipping. The mass of the loaded truck with mass center at G is 1900 kg. Problem 6/119 (a) Torque required to roll the front wheels over the curbing ● Calculation Process 1. Identify Given Values and Geometry: Mass of the truck: Weight of the truck: Curb height: Height of center of mass : Horizontal distance from to front axle: Horizontal distance from to rear axle: Total wheelbase: Wheel radius (assumed from standard problem data for this configuration): 2. Determine Contact Angle at the Curb: The angle from the vertical to the point of contact on the curb is given by: Horizontal distance from front axle to curb corner: M m=1900 kg W=mg=1900×9.81=18639 N h=130 mm=0.13 m Gh = G 650 mm=0.65 m G1200 mm=1.2 m G1600 mm=1.6 m L=1.2+1.6=2.8 m r= 325 mm=0.325 m θθ cosθ= = r r−h = 325 325−130 = 325 195 0.6 sinθ= = 1−0.6 2 0.8⟹tanθ= = 0.6 0.8 3 4 d=rsinθ=325×0.8= 260 mm=0.26 m 3. Establish Equilibrium Equations: At the verge of rolling over, the normal force on the front wheels is zero (). Since front wheels are idlers, the curb reaction must be radial. From the equilibrium of the whole truck, let be the normal force and be the friction force at the rear wheels: Dividing the