three forces of magnitude 6N, 2N and 3N act on a small object in directions north, south and west respectively, find magnitude of the resultant force
r = <0,6>+<0,-2>+<-3,0> = <-3,4>
|r| = 5
Fr = 6i-2i-3 = -3+4i.
Fr = sqrt(3^2+4^2) = 5 N.
To find the magnitude of the resultant force, we need to use vector addition. We can calculate the resultant force by adding the individual forces together.
Let's assume the force acting north as F1, the force acting south as F2, and the force acting west as F3.
F1 = 6N (north)
F2 = 2N (south)
F3 = 3N (west)
To calculate the resultant force, we can use the Pythagorean theorem as follows:
Resultant force (F) = √(F1^2 + F2^2 + F3^2)
F = √((6N)^2 + (2N)^2 + (3N)^2)
F = √(36N^2 + 4N^2 + 9N^2)
F = √(49N^2)
F = 7N
Therefore, the magnitude of the resultant force is 7N.
To find the magnitude of the resultant force, we can use vector addition.
First, let's represent the forces as vectors:
- The force of 6N to the north can be represented as a vector, let's call it F1, with a magnitude of 6N and pointing upwards (in the positive y-direction).
- The force of 2N to the south can also be represented as a vector, let's call it F2. However, since it is in the opposite direction, it will have a magnitude of -2N and will point downwards (in the negative y-direction).
- The force of 3N to the west can be represented as a vector, let's call it F3, with a magnitude of 3N and pointing towards the west (in the negative x-direction).
Now, let's add the three vectors using vector addition:
Resultant force, F = F1 + F2 + F3
To find the resultant force, we add the x-components and y-components of the vectors separately:
Fx = F1x + F2x + F3x
Fy = F1y + F2y + F3y
Since F1 and F2 are in the y-direction, their x-components will be zero. Similarly, F3 is in the x-direction, so its y-component will be zero.
Therefore, the x-component of the resultant force will be F3x = -3N and the y-component will be F1y + F2y = 6N - 2N = 4N.
To find the magnitude of the resultant force, we use the Pythagorean theorem:
Magnitude of the resultant force, |F| = sqrt(Fx^2 + Fy^2)
|F| = sqrt((-3N)^2 + (4N)^2)
|F| = sqrt(9N^2 + 16N^2)
|F| = sqrt(25N^2)
|F| = 5N
Therefore, the magnitude of the resultant force is 5N.