Four forces of magnitude 10N 5N 4N and 6N act on an object in the direction of north west east and south respectively find the magnitude and direction of their resultant
the resultant is -i+4j = √17 N in the direction
NθW where tanθ = 4, or in the direction N14°W
answered is wrong again and oobleck is right again !
To find the magnitude and direction of the resultant force from the given forces, you need to use vector addition.
Step 1: Convert the given forces into vector form. Remember that vectors have both magnitude and direction.
Given forces:
10N towards north (N)
5N towards west (W)
4N towards east (E)
6N towards south (S)
Step 2: Represent each force as a vector.
10N towards north (N) can be represented as a vector:
10N * North (N)
= 10N * (0, 1)
5N towards west (W) can be represented as a vector:
5N * West (W)
= 5N * (-1, 0)
4N towards east (E) can be represented as a vector:
4N * East (E)
= 4N * (1, 0)
6N towards south (S) can be represented as a vector:
6N * South (S)
= 6N * (0, -1)
Step 3: Add all the vectors to get the resultant vector.
Resultant vector = (10N * (0, 1)) + (5N * (-1, 0)) + (4N * (1, 0)) + (6N * (0, -1))
Step 4: Simplify the resultant vector.
Resultant vector = (0, 10N) + (-5N, 0) + (4N, 0) + (0, -6N)
= (4N, 4N)
Step 5: Find the magnitude of the resultant vector.
Magnitude of the resultant vector = sqrt((4N)^2 + (4N)^2)
= sqrt(16N^2 + 16N^2)
= sqrt(32N^2)
= 4N * sqrt(2)
Therefore, the magnitude of the resultant force is 4N * sqrt(2).
Step 6: Find the direction of the resultant vector.
The direction of the resultant vector can be determined using trigonometry.
tan(theta) = (4N / 4N)
tan(theta) = 1
theta = arctan(1)
Since the forces are directed towards north-west, east, and south, the resultant force is directed in the south-east direction.
Therefore, the direction of the resultant force is South-East.
To summarize, the magnitude of the resultant force is 4N * sqrt(2) and it is directed towards the South-East direction.