Question

forces of F1 = 975 N, and f2 = 745 N, and F3 = 1175 N are applied to the same point. F1 points at 53.9-deg, F2 points at 212.8-deg, and F3 points at 301.6-deg. Find the direction of the resultant force

Answer 1

The direction of the resultant force is 132.01 degrees.

Step-by-step explanation:

The direction of the resultant force can be found by adding the x and y components of the given forces. First, let's find the x and y components of each force:

• F1x = 975 * cos(53.9) = 625.62 N
• F1y = 975 * sin(53.9) = 748.2 N
• F2x = 745 * cos(212.8) = -417.97 N
• F2y = 745 * sin(212.8) = -525.95 N
• F3x = 1175 * cos(301.6) = -919.75 N
• F3y = 1175 * sin(301.6) = 586.53 N

Next, we can add the x and y components together to find the resultant force:

• Resultant force in the x-direction: 625.62 N - 417.97 N - 919.75 N = -712.1 N
• Resultant force in the y-direction: 748.2 N - 525.95 N + 586.53 N = 808.78 N

The magnitude of the resultant force can be found using the Pythagorean theorem:

Magnitude of the resultant force = sqrt((-712.1 N)^2 + (808.78 N)^2) = 1053.43 N

The angle of the resultant force can be found using the inverse tangent function:

Angle of the resultant force = atan(808.78 N / -712.1 N) = 132.01 degrees

Therefore, the direction of the resultant force is 132.01 degrees.