three forces act on a body.forceof 30N and 25N act to east and a force of 40N acts to the west.draw a fully labelled scale vector diagram to find the magnitude and direction resultant force use 1 mm : 1N.
Fr = 30 + 25 + (-40) = 15 N.,Headed East
To find the magnitude and direction of the resultant force, we can use a scale vector diagram. Here's how you can draw the fully labeled scale vector diagram:
1. Start by drawing a reference line in the desired direction. In this case, since the 30N and 25N forces are acting to the east and the 40N force is acting to the west, draw a horizontal line from left to right.
2. Label the reference line with an arrowhead pointing to the right to indicate the positive direction (east).
3. Choose a convenient scale for the diagram. In this case, you mentioned using 1 mm : 1N. This means that for every 1 mm on the diagram, it represents 1 Newton of force.
4. To represent the 30N force, measure 30 mm from the beginning of the reference line (left side) and draw an arrowhead pointing to the right. Label it as "30N" for clarity.
5. Next, represent the 25N force. Starting from the tip of the previous force arrow, measure an additional 25 mm to the right and draw a new arrowhead pointing to the right. Label it as "25N".
6. Now, represent the 40N force acting to the left (west). Starting from the beginning of the reference line (left side), measure 40 mm to the left this time. Draw an arrowhead pointing to the left (opposite to the positive direction). Label it as "40N".
7. To find the resultant force, draw a closing line from the beginning of the reference line (left side) to the tip of the last force arrow (40N arrow). This line represents the vector addition of the three forces.
8. Measure the length of the resultant force line (closing line) using the same scale. The length of the line will represent the magnitude of the resultant force.
9. Finally, determine the direction of the resultant force. Measure the angle between the reference line and the resultant force line using a protractor, with the protractor's baseline aligned with the reference line. This angle will represent the direction of the resultant force.
Note: If the forces are not at perpendicular angles, you may need to use trigonometric methods to find the magnitude and direction of the resultant force accurately.
By following these steps and using the provided scale, you should be able to draw a fully labeled scale vector diagram to find the magnitude and direction of the resultant force.