Thursday, June 28, 2007
Graphical Method
Materials used:
Pencil, Ruler and Protractor
Definition:
Graphical method – is the method used by using tools such as ruler and protractor to get the resultant vector.
The simplest use of vectors and calculation by means of vectors is illustrated in the diagram, drawn to represent a boat moving across a stream. Vector a~, or A, indicates the motion of the boat in the course of a given interval of time if it were moving through still water; vector b~, or $, shows the drift or flow of the current during the same period of time. The actual path of travel of the boat under the influence of its own propulsion and of the current is represented by vector c~, or B. By the use of vectors any type of problem involving the motion of an object being acted on by several forces can be solved graphically.
This method of problem solution, known as vector addition, is performed as follows. A vector representing one force is drawn from the origin O in the proper direction. The length of the vector is made to agree with any convenient arbitrary scale, such as a given number of centimeters to the kilometers. In the diagram the rate of rowing was 2.2 km/h, the time rowed was 1 hr, and the scale is 1 cm to 1 km. Therefore, the line A is drawn as 2.2 cm to represent 2.2 km. The river current speed of 6 km/h is then represented by a vector $ that is 6 cm long, indicating a distance of 6 km that the current moved during 1 hr. This second vector is drawn with its origin at the end of vector a~ in a direction parallel to the flow of the current. The point B at the end of the second vector represents the actual position of the boat at the end of 1 hr of travel, and the actual distance traveled is represented by the length (in this case, about 6.4 km) of the vector c~, or B.
Procedure:
First convert the given units to smaller units to represent it much smaller.
` Ex. 200ft – Convert it to – 1cm = 20ft. So the measurement of the line will be 10cm.
Second After converting it, analyze the given data.
Ex. Line AD -200 ft. horizontally –
this given means that a line must be drawn horizontally.
3rd step is to analyze what is the direction and the degree given to a particular line.
Ex. 135 ft. at an angle of 30 degree above horizontal.
Next is proceed and draw the other dimensions and lines.
After completing the drawing you must record all the data’s.
Ex.
6. Find the resultant vector by measuring it by the protractor.
Answer is 45 degree 900ft = 45 cm
Source: Microsoft ® Encarta ® Premium Suite 2005. © 1993-2004 Microsoft Corporation. All rights reserved.
