Trigonometry and Solving Physics Problems
In physics, most problems are solved much more easily when a free body diagram is used. Free body diagrams use geometry and vectors to visually represent the problem. Trigonometry is also used in determining the horizontal and vertical components of forces and objects. Free body diagrams are very helpful in visually identifying which components are unknown and where the moments are applied. They can help analyze a problem, whether it is static or dynamic.
When people draw free body diagrams, often not everything is perfectly parallel and perpendicular. Sometimes people need to analyze the horizontal and vertical components of forces and object orientation. When the force or object is not acting parallel to the x or y axis, people can employ basic trigonometry to use the simplest components of the action to analyze it. Basically, everything should be considered in terms of x and y, which sometimes takes some manipulation .
Free Body Diagram
The rod is hinged from a wall and is held with the help of a string.
A rod 'AB' is hinged at 'A' from a wall and is held still with the help of a string, as shown in . This exercise involves drawing the free body diagram. To make the problem easier, the force F will be expressed in terms of its horizontal and vertical components . Removing all other elements from the image helps produce the finished free body diagram .
Free Body Diagram
The free body diagram as a finished product
Given the finished free body diagram, people can use their knowledge of trigonometry and the laws of sine and cosine to mathematically and numerical represent the horizontal and vertical components:
.