Mathematically determine the resultant force if two forces A and B act on an object. Force A is 85N and is at an angle of 20• to the horizontal. Force B is 125N and is at an angle of 60• to the horizontal.
2014
I dont understand
Well, well, well, it seems like we have a combination of forces going on here! Let's do some math and find the resultant force, shall we?
To determine the resultant force, we need to break down these forces into their horizontal and vertical components. So, let's get crackin'!
For Force A, we have an angle of 20° to the horizontal. That means the horizontal component of Force A will be A * cos(20°), and the vertical component will be A * sin(20°).
For Force B, which is at an angle of 60° to the horizontal, the horizontal component will be B * cos(60°), and the vertical component will be B * sin(60°).
Now, let's calculate these components (I promise no funny business with these calculations!):
Horizontal component of Force A = 85N * cos(20°)
Vertical component of Force A = 85N * sin(20°)
Horizontal component of Force B = 125N * cos(60°)
Vertical component of Force B = 125N * sin(60°)
Once we have these components, we can find the resultant horizontal and vertical forces by adding them up:
Resultant horizontal force = Horizontal component of Force A + Horizontal component of Force B
Resultant vertical force = Vertical component of Force A + Vertical component of Force B
Then, the resultant force can be found using the Pythagorean theorem:
Resultant force = sqrt((Resultant horizontal force)^2 + (Resultant vertical force)^2)
And voila! You've got your resultant force, my friend. Math can be a circus sometimes, but we managed to tame it this time!
To determine the resultant force when two forces act on an object, we can use the concept of vector addition.
Step 1: Convert angles to components
First, we need to convert the given angles to their respective horizontal (x-axis) and vertical (y-axis) components. To do this, we use trigonometry.
For Force A:
Angle A = 20°
Horizontal Component A (Ax) = A * cos(Angle A)
Vertical Component A (Ay) = A * sin(Angle A)
For Force B:
Angle B = 60°
Horizontal Component B (Bx) = B * cos(Angle B)
Vertical Component B (By) = B * sin(Angle B)
Step 2: Find the resultant components
To find the resultant force, we add the horizontal and vertical components of both forces:
Resultant Horizontal Component (Rx) = Ax + Bx
Resultant Vertical Component (Ry) = Ay + By
Step 3: Calculate the magnitude and angle of the resultant force
Using the resultant components, we can find the magnitude (R) and angle (θ) of the resultant force:
Magnitude of the Resultant Force (R) = √(Rx^2 + Ry^2)
Angle of the Resultant Force (θ) = tan^(-1)(Ry / Rx)
Now, let's calculate the resultant force using the given values:
Force A = 85N
Angle A = 20°
Force B = 125N
Angle B = 60°
Calculating the components:
Ax = 85 * cos(20°)
Ay = 85 * sin(20°)
Bx = 125 * cos(60°)
By = 125 * sin(60°)
Calculating the resultant components:
Rx = Ax + Bx
Ry = Ay + By
Calculating the magnitude and angle of the resultant force:
R = √(Rx^2 + Ry^2)
θ = tan^(-1)(Ry/Rx)
By substituting the values, we can determine the resultant force.
Answer question
matmatically
F(A)x =F(A) •cos20°
F(A)y= F(A) •sin20°
F(B)x =F(B) •cos80°
F(B)y= F(B) •sin60°
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Fx=F(A)x+F(B)x = F(A) •cos20°+F(B) •cos80° = 85 •cos20°+125 •cos80°=…
Fy=F(A)y+F(B)y = F(A) •sin20°+F(B) •sin80°=85 •sin20°+125 •sin80°=...
F=sqrt(Fx²+Fy²) =...