Two force,3N and 4N act on a body in the direction due north and east respectively. Calculate their equilibrium?
force resultant: 4i+3j
equilibrium force: -(4i+3j)
5N 53 degrees East of north
To calculate the equilibrium of the two forces, we need to find the resultant force by combining the two forces acting on the body. The resultant force can be found using vector addition.
First, we need to break down the forces into their respective x and y components. The force of 3N acting due north can be considered as having a y-component of 3N, and no x-component. The force of 4N acting due east can be considered as having an x-component of 4N, and no y-component.
Now, we can find the resultant force by adding the x-components and the y-components separately. Since the forces act perpendicular to each other, the x and y components are independent and can be added directly.
In the x-direction:
Resultant x-component = 4N (due east)
In the y-direction:
Resultant y-component = 3N (due north)
Therefore, the resultant force is the combination of these x and y components:
Resultant force = square root of (Resultant x-component^2 + Resultant y-component^2)
Plugging in the values:
Resultant force = square root of (4^2 + 3^2) = square root of (16 + 9) = square root of 25 = 5N
Hence, the equilibrium of the two forces is 5N.