Question 1178041: The resultant force of F1(150N, 030) and F2( x N, 120) is R(y N, 090). Find, correct to two decimal places, the values of x and y
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's solve this problem step-by-step.
**1. Resolve Forces into Components**
* **F1 (150N, 030°):**
* F1x = 150 * cos(30°) = 150 * (√3 / 2) ≈ 129.90 N
* F1y = 150 * sin(30°) = 150 * (1/2) = 75 N
* **F2 (x N, 120°):**
* F2x = x * cos(120°) = x * (-1/2) = -x/2 N
* F2y = x * sin(120°) = x * (√3 / 2) ≈ 0.866x N
* **R (y N, 090°):**
* Rx = y * cos(90°) = y * 0 = 0 N
* Ry = y * sin(90°) = y * 1 = y N
**2. Set Up Equations for Resultant Force**
The resultant force is the vector sum of the individual forces:
* Rx = F1x + F2x
* Ry = F1y + F2y
Substitute the component values:
* 0 = 129.90 - x/2
* y = 75 + 0.866x
**3. Solve for x**
From the first equation:
* x/2 = 129.90
* x = 129.90 * 2
* x = 259.80 N
**4. Solve for y**
Substitute the value of x into the second equation:
* y = 75 + 0.866 * 259.80
* y = 75 + 224.9928
* y = 299.9928 N
**5. Round to Two Decimal Places**
* x ≈ 259.80 N
* y ≈ 299.99 N
**Therefore:**
* x ≈ 259.80 N
* y ≈ 299.99 N
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