when will the resultant of the two vectors be at maximum when two forces of 5n and 7n act on an object?
When they are both in the same direction and therefore add.
|R| = |A| |B| cos theta
|cos theta| </= 1 for all theta and is max of 1 when theta = 0
5+7 = 12
If theta is the angle between vectors.
yes
To find when the resultant of two vectors is at its maximum, you need to determine the direction in which the vectors are added. This is because the magnitude (force) alone does not give enough information to determine the maximum resultant.
The resultant magnitude is maximized when the two vectors are aligned or in the same direction. This is known as the principle of superposition.
In this case, the two forces are 5 N and 7 N. To find the resultant force, you need to add these two vectors together. You can do this using vector addition.
Let's represent the 5 N force as vector A and the 7 N force as vector B. To add these vectors, you can use either graphical or algebraic methods. Let's use the graphical method for illustration.
1. Scale and draw vector A:
- Choose a suitable scale for your diagram. For example, you can assign a length of 1 cm to represent 1 N.
- Use a ruler to draw a line segment to represent vector A. The length of this line segment should be proportional to the magnitude of vector A (5 N).
2. Scale and draw vector B:
- Again, use your scale to draw a line segment to represent vector B. The length of this line segment should be proportional to the magnitude of vector B (7 N).
- Start the tail of vector B at the head of vector A.
3. Complete the parallelogram:
- Draw a line segment from the tail of vector A to the head of vector B. This represents the resultant vector.
4. Measure the magnitude and direction of the resultant vector:
- Use a ruler to measure the length of the resultant vector. This represents the magnitude of the resultant force.
- Measure the angle between the resultant vector and vector A. This represents the direction of the resultant force.
By following these steps, you can determine the maximum resultant force when two forces of 5 N and 7 N act on an object.