Forces of 23 N and 41 N act at a point and are inclined at 90° to each other. Find, by drawing, the resultant force and its direction relative to the 41 N force.
the resultant has magnitude
√(23^2 + 41^2)
and direction θ where
tanθ = 23/41
Draw the triangle
force=sqrt(23^2+41^2)
angle=arctan(23/41)
To find the resultant force and its direction, we can use the graphical method of vector addition. Here are the steps to do it:
Step 1: Draw a line to represent the 41 N force. Label it as F1.
Step 2: Draw another line to represent the 23 N force. Label it as F2.
Step 3: Starting from the tail of F1, draw F2 in the direction specified by the angle between the forces (90°). The tail of F2 should meet the head of F1.
Step 4: Draw a straight line from the tail of F1 to the head of F2. This line represents the resultant force, labeled as R.
Step 5: Measure the length of R using a ruler.
Step 6: Use a protractor to measure the angle between the resultant force (R) and the 41 N force (F1). This will give you the direction of the resultant force relative to F1.
Step 7: Label the length of R and the angle between R and F1 on the diagram.
Step 8: If necessary, calculate the numerical value of the resultant force and the angle using trigonometry.
Using these steps, you can visually determine the resultant force and its direction relative to the 41 N force.
To find the resultant force and its direction relative to the 41 N force, we can use a graphical method known as the parallelogram law of vector addition. Here's how to do it:
1. Draw a line segment to represent the 41 N force, starting from an arbitrary point.
2. Draw another line segment to represent the 23 N force, starting from the same point.
3. Using a ruler, draw a parallelogram with the 41 N and 23 N force as adjacent sides. The starting point of the 23 N force should coincide with the endpoint of the 41 N force.
4. Complete the parallelogram by drawing the remaining two sides.
5. The diagonal of the parallelogram, drawn from the starting point of the 41 N force to the opposite corner, represents the resultant force.
6. Measure the length of the diagonal using a ruler. Let's say it measures 54 N.
7. The direction of the resultant force relative to the 41 N force can be determined by drawing a line from the starting point of the 41 N force to the end point (tip) of the diagonal.
8. To measure the angle between the 41 N force and the resultant force, use a protractor. Place the protractor with its center at the starting point of the 41 N force and align one of its sides with the line drawn in the previous step. Read the angle measurement where the line intersects the protractor. Let's say it measures 30°.
Therefore, the resultant force has a magnitude of 54 N (measured from the drawing) and is inclined at an angle of 30° relative to the 41 N force.