The sum of two forces, one having a magni- tude of 9 N acting due east and other having a magnitude of 4 N acting due north is
To find the sum of these two forces, we can use vector addition.
Step 1: Draw a diagram to represent the forces.
North (up)
|
4 N |
|
|
|
|
-------------------------------- East (right)
9 N
Step 2: Label the forces. Let's call the force acting due east 9 N as force A and the force acting due north 4 N as force B.
Step 3: Draw a vector triangle. Place force A horizontally towards the right and force B vertically upwards.
North (up)
|
4 N |
|
|
|
|
\
\
\
9 N - - - \ - - - East (right)
Step 4: Complete the triangle to form a right triangle by connecting the endpoints of force A and force B.
North (up)
|
4 N | \
| \
| \
|----------\
| /
/
9 N / - - East (right)
Step 5: Measure the sides of the triangle. The horizontal side (base) represents the magnitude of the force acting due east (9 N), and the vertical side (height) represents the magnitude of the force acting due north (4 N).
Step 6: Use the Pythagorean theorem to find the magnitude of the resultant force (sum). The Pythagorean theorem states that the square of the hypotenuse (resultant force) is equal to the sum of the squares of the other two sides.
By applying the Pythagorean theorem:
resultant force^2 = 9 N^2 + 4 N^2
resultant force^2 = 81 N^2 + 16 N^2
resultant force^2 = 97 N^2
Taking the square root of both sides, we find:
resultant force ≈ √97 ≈ 9.849 N
Step 7: Determine the direction of the resultant force. To find the direction of the resultant force, we can use trigonometry. The angle θ can be found using the equation:
θ = tan^(-1)(Opposite/Adjacent)
θ = tan^(-1)(4 N/9 N)
θ ≈ 24.26 degrees
Therefore, the resultant force has a magnitude of approximately 9.849 N and acts at an angle of approximately 24.26 degrees with respect to the positive x-axis (east).
To find the sum of two forces, one with a magnitude of 9 N acting due east and the other with a magnitude of 4 N acting due north, we can use vector addition.
Step 1: Draw a diagram representing the forces. Draw an arrow pointing east with a length representing 9 units (9 N of magnitude) and another arrow pointing north with a length representing 4 units (4 N of magnitude).
Step 2: Choose a suitable scale for the diagram. For instance, you can assign 1 centimeter to represent 1 Newton.
Step 3: Measure and draw the first force due east. Label it as F1 = 9 N.
Step 4: Measure and draw the second force due north. Label it as F2 = 4 N.
Step 5: To find the sum of these two forces, draw a new arrow starting from the origin (where the two forces originate) and ending at the point where the two forces intersect. This new arrow represents the resultant vector, which is the sum of the two forces.
Step 6: Measure the length of the resultant vector and find its magnitude.
In this case, we have a right-angled triangle formed by the two forces. We can use the Pythagorean theorem to find the magnitude of the resultant vector.
Using the Pythagorean theorem:
(Resultant magnitude)^2 = (F1 magnitude)^2 + (F2 magnitude)^2
(Resultant magnitude)^2 = (9 N)^2 + (4 N)^2
(Resultant magnitude)^2 = 81 N^2 + 16 N^2
(Resultant magnitude)^2 = 97 N^2
Taking the square root of both sides gives:
Resultant magnitude = √(97 N^2) ≈ 9.85 N
Therefore, the sum of the two forces is approximately 9.85 N in magnitude. The direction of the sum can be obtained by measuring the angle the resultant vector makes with the eastward direction.