2.6:

Two-Dimensional Force System

JoVE 핵심
Mechanical Engineering
JoVE 비디오를 활용하시려면 도서관을 통한 기관 구독이 필요합니다.  전체 비디오를 보시려면 로그인하거나 무료 트라이얼을 시작하세요.
JoVE 핵심 Mechanical Engineering
Two-Dimensional Force System

640 Views

01:20 min

September 22, 2023

A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:

Equation 1

where Fx and Fy are the vector components of F in the x and y directions, respectively. Each of these vector components can be represented as a scalar (Fx and Fy) times the appropriate unit vector.

To determine the components of the force vector in a Cartesian coordinate system, one must first determine the angle θ that the force makes with the positive x-axis. Assuming that the line of action of the force passes through the origin, its components can be expressed in the Cartesian form using basic trigonometry.

Equation 2

where F denotes the magnitude of the force vector. The direction of the force vector is given by the inverse of the tangent of the ratio of its components.

Equation 3

However, in cases where the line of action of the force vector does not pass through the origin, its vector components can still be expressed in Cartesian form using the same approach. We can choose the sign of each component based on the direction of the force vector. By resolving the force vector into its components, we can determine the force's net effect on the structure in question.

Understanding the two-dimensional force system is critical for engineers to analyze and design structures that are safe and structurally sound. This knowledge provides the foundational understanding of how a structure will react to various forces and helps pinpoint the design weaknesses, if any.