Meriam, Kraige & Bolton — Statics of Particles: Problem 2_142

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/142 While cutting a piece of paper, a person exerts the two indicated forces on a paper cutter. Reduce the two forces to an equivalent force–couple system at corner O and then specify the coordinates of the point P in the x-y plane through which the resultant of the two forces passes. The cutting surface is 24′′ × 24′′. Problem 2/142 1. Coordinate Analysis and Point Identification First, we establish a coordinate system with the origin at point as indicated in the diagram. Based on the "24′′ × 24′′" board dimensions and the provided labels: The x-axis lies along the left edge of the board. The y-axis lies along the front edge of the board. The z-axis is vertical, pointing upwards. The cutting blade is situated along the right edge of the board at . We identify the application points for the two downward forces: Point A (27-lb force): From the diagram, it is located from the hinge? No, let's use the dimensions from the origin . The tip of the handle is from the front edge (-axis) in the -direction, and point is further back. Point lies on the blade edge, so its -coordinate is the board width: Thus, . Point B (8-lb force at handle tip): The tip is from the front edge: The handle has a offset from the board edge at the tip: O y=24 in 11 in+7 in+5 in=23 in O 5 inyxA7 in x = A 5 in+7 in=12 in Ay y = A 24 in r = A 12i+24j in 5 in x = B 5 in 1 in Thus, . 2. Equivalent Resultant Force Both forces act vertically downwards in the negative