Two forces 7N each are inclined at an angle of 120 degree to each other. Find the single force that will replace the given force system
well, it will be along the 60 degree ray
force=14cos60
120 degree, 10 North
To find the single force that will replace the given force system, we need to use the concept of vector addition.
Step 1: Resolve the given forces into their horizontal and vertical components.
Considering one force as F1 and the other as F2:
F1 = 7 N
F2 = 7 N
Angle between F1 and the x-axis = 120 degrees
Angle between F2 and the x-axis = 120 degrees
The horizontal component of a force can be found using:
Fx = F * cos(theta), where F is the magnitude of the force and theta is the angle it makes with the x-axis.
The vertical component of a force can be found using:
Fy = F * sin(theta), where F is the magnitude of the force and theta is the angle it makes with the x-axis.
Substituting the values, we have:
F1x = 7 N * cos(120 degrees)
F1y = 7 N * sin(120 degrees)
F2x = 7 N * cos(120 degrees)
F2y = 7 N * sin(120 degrees)
Step 2: Add the horizontal and vertical components of the forces separately.
Taking the horizontal components:
Fx = F1x + F2x
Taking the vertical components:
Fy = F1y + F2y
Step 3: Combine the horizontal and vertical components to get the resultant force.
To find the magnitude of the resultant force, use the Pythagorean theorem:
R = sqrt(Fx^2 + Fy^2)
To find the angle of the resultant force, use the inverse tangent (arctan) function:
theta = arctan(Fy / Fx)
Substituting the values obtained in step 2:
Fx = (7 N * cos(120 degrees)) + (7 N * cos(120 degrees))
Fy = (7 N * sin(120 degrees)) + (7 N * sin(120 degrees))
Finally, substituting the values obtained in step 3:
R = sqrt(Fx^2 + Fy^2)
theta = arctan(Fy / Fx)
Calculate the above expressions to find the magnitude and angle of the resultant force.