Forces of F1=975 N,F2= 745 N, f3= 1175 N and are applied at the same point. The angle between f1 and f2 is 60.0 degree and the angle between f2 and f3 is 30.0 degree. F2 is between f1 and f3 find the resultant force.
Fr = 975N[0o] + 745N[60o] + 1175N[90o]
X=975 + 745*cos60 + 1175*cos90=1347.5 N
Y = 745*sin60 + 1175*sin90 = 1820.2 N.
tan A = Y/X = 1820.2/1347.5 = 1.31079
A = 53.5o
Fr = Y/sin A = 1820.2/sin53.5=2264.3 N.
[53.5o].
Well, well, well. It seems like we have a little force party going on here. Let's calculate the resultant force and see what we get.
First, we need to break down the forces into their horizontal and vertical components. So grab your imaginary hammer and let's smash these forces into pieces!
For F1, the horizontal component (F1x) will be F1 * cos(0 degrees), which is just F1 since cos(0 degrees) is 1. The vertical component (F1y) will be F1 * sin(0 degrees), which is 0 because sin(0 degrees) is 0. So, F1x = 975 N and F1y = 0 N.
For F2, we need to do some trigonometry magic. The horizontal component (F2x) will be F2 * cos(60 degrees). And the vertical component (F2y) will be F2 * sin(60 degrees). So, F2x = 745 N * cos(60 degrees) and F2y = 745 N * sin(60 degrees). I'll leave you to calculate those values.
Now, let's move on to F3. Again, trigonometry is our friend here. The horizontal component (F3x) will be F3 * cos(30 degrees), and the vertical component (F3y) will be F3 * sin(30 degrees). Go ahead and calculate those values too.
Once we have the horizontal and vertical components for each force, we can add them up separately. The horizontal component of the resultant force (Rx) will be the sum of F1x, F2x, and F3x. And the vertical component (Ry) will be the sum of F1y, F2y, and F3y.
Finally, we can use the Pythagorean theorem to find the magnitude of the resultant force (R). R^2 = Rx^2 + Ry^2. Just plug in the values we calculated and solve for R.
Voila! You've got your resultant force. I hope all this force math didn't make your head spin too much.
To find the resultant force, we can use vector addition. Let's break down each force into its x and y components.
Given:
F1 = 975 N
F2 = 745 N
F3 = 1175 N
Angle between F1 and F2 = 60 degrees
Angle between F2 and F3 = 30 degrees
To calculate the x and y components of each force, we will use the following equations:
F_x = F * cos(theta)
F_y = F * sin(theta)
Calculating F1's components:
F1_x = 975 N * cos(60)
F1_x ≈ 975 N * 0.5
F1_x ≈ 487.5 N
F1_y = 975 N * sin(60)
F1_y ≈ 975 N * (√3/2)
F1_y ≈ 487.5 N * √3
F1_y ≈ 844.3 N
Calculating F2's components:
Since F2 is between F1 and F3, we can simply take negative values of F1's components.
F2_x = - F1_x
F2_x = - 487.5 N
F2_y = - F1_y
F2_y = - 844.3 N
Calculating F3's components:
F3_x = 1175 N * cos(30)
F3_x ≈ 1175 N * (√3/2)
F3_x ≈ 1175 N * 0.866
F3_x ≈ 1018.1 N
F3_y = 1175 N * sin(30)
F3_y ≈ 1175 N * 0.5
F3_y ≈ 587.5 N
Now we can calculate the resultant force:
R_x = F1_x + F2_x + F3_x
R_x = 487.5 N - 487.5 N + 1018.1 N
R_x ≈ 1018.1 N
R_y = F1_y + F2_y + F3_y
R_y = 844.3 N - 844.3 N + 587.5 N
R_y ≈ 587.5 N
To find the magnitude of the resultant force:
R = √(R_x^2 + R_y^2)
R = √(1018.1 N^2 + 587.5 N^2)
R ≈ √(1036472.6 N^2)
R ≈ 1018.1 N
Therefore, the magnitude of the resultant force is approximately 1018.1 N.
To find the resultant force, we need to calculate the vector sum of the given forces.
First, let's decompose each force into its horizontal and vertical components using trigonometry.
For F1:
F1x = F1 * cos(angle1)
F1y = F1 * sin(angle1)
For F2:
F2x = F2 * cos(angle2)
F2y = F2 * sin(angle2)
For F3:
F3x = F3 * cos(angle3)
F3y = F3 * sin(angle3)
Next, let's calculate the horizontal and vertical components for F2 as it is between F1 and F3:
F2x = F1x + F3x
F2y = F1y + F3y
Now, we can calculate the resultant force by summing up the horizontal and vertical components:
Resultant force (Rx) = F1x + F2x + F3x
Resultant force (Ry) = F1y + F2y + F3y
Finally, we can calculate the magnitude and direction of the resultant force using the Pythagorean theorem and inverse trigonometric functions:
Resultant force (R) = sqrt((Rx)^2 + (Ry)^2)
Angle (θ) = tan^(-1)(Ry / Rx)
Plugging in the values for F1, F2, F3, angle1, angle2, and angle3, we can calculate the resultant force and its angle.