Forces F\(_1\)(10N, 090°) and F\(_2\)(20N, 210\(^o\)) and (4N,330°) act on a particle, Find, correct to one decimal place, the magnitude of the resultant fo...
Forces F\(_1\)(10N, 090°) and F\(_2\)(20N, 210\(^o\)) and (4N,330°) act on a particle, Find, correct to one decimal place, the magnitude of the resultant force.
To find the magnitude of the resultant force, we need to first calculate the x and y components of each force.
For F1:
The magnitude is 10 N
The angle is 90 degrees
The x component is 10 cos(90) = 0 N
The y component is 10 sin(90) = 10 N
For F2:
The magnitude is 20 N
The angle is 210 degrees
The x component is 20 cos(210) = -17.3 N (negative because it points to the left)
The y component is 20 sin(210) = -10 N (negative because it points downwards)
For F3:
The magnitude is 4 N
The angle is 330 degrees
The x component is 4 cos(330) = 3.5 N (positive because it points to the right)
The y component is 4 sin(330) = -2 N (negative because it points downwards)
To find the total x and y components, we can add up the individual x and y components:
The total x component is 0 - 17.3 + 3.5 = -13.8 N
The total y component is 10 - 10 - 2 = -2 N
To find the magnitude of the resultant force, we can use the Pythagorean theorem:
resultant force = sqrt((-13.8)^2 + (-2)^2) = 13.9 N
Therefore, the magnitude of the resultant force is 13.9 N.