Three forces with magnitudxes 100, 50 and 80 lbs act on an object at angles of 50 degree, 160 degree and -20 degree respectively.
I assume you want the resultant force? Just convert the polar coordinates to rectangular, add them, and convert back to polar:
(100,50°) = (64.28,76.60)
(50,160°) = (-46.98,17.10)
(80,-20°) = (75.18,-27.36)
add them to get
(92.48,66.34) = (113.81,35.65°)
To find the resultant force on the object, we need to calculate the horizontal and vertical components of each force and then sum them up.
Let's break down the forces given:
Force 1: Magnitude = 100 lbs, angle = 50 degrees
Force 2: Magnitude = 50 lbs, angle = 160 degrees
Force 3: Magnitude = 80 lbs, angle = -20 degrees
To find the horizontal and vertical components of each force, we can use trigonometry. Recall that cosine gives the horizontal component and sine gives the vertical component.
For Force 1:
Horizontal component of Force 1 = 100 lbs * cos(50 degrees)
Vertical component of Force 1 = 100 lbs * sin(50 degrees)
For Force 2:
Horizontal component of Force 2 = 50 lbs * cos(160 degrees)
Vertical component of Force 2 = 50 lbs * sin(160 degrees)
For Force 3:
Horizontal component of Force 3 = 80 lbs * cos(-20 degrees)
Vertical component of Force 3 = 80 lbs * sin(-20 degrees)
Now that we have the horizontal and vertical components for each force, we can sum them up. The sum of the horizontal components will give us the horizontal component of the resultant force, and the sum of the vertical components will give us the vertical component of the resultant force.
Horizontal component of the resultant force = (Horizontal component of Force 1) + (Horizontal component of Force 2) + (Horizontal component of Force 3)
Vertical component of the resultant force = (Vertical component of Force 1) + (Vertical component of Force 2) + (Vertical component of Force 3)
Once we have the horizontal and vertical components of the resultant force, we can use Pythagoras' theorem to calculate the magnitude of the resultant force:
Magnitude of the resultant force = sqrt((Horizontal component of the resultant force)^2 + (Vertical component of the resultant force)^2)
So, by plugging in the values for each component, we can find the magnitude of the resultant force.