Answer :
When adding the forces F1, F2, and F3 together, the resultant force has a magnitude of 89.3 lbs and is oriented at an angle of 52.6° counterclockwise from the positive x-axis.
To find the resultant force from adding F1, F2, and F3, we can use vector addition. Each force can be represented as a vector, with magnitude and direction. The magnitude of each force is given, along with its angle measured counterclockwise from the positive x-axis.
First, let's convert the given angles to standard position angles (measured counterclockwise from the positive x-axis). We subtract each angle from 360° to get the standard position angle: F1: 360° - 65° = 295° F2: 360° - 125° = 235° F3: 360° - 285° = 75°
Now, we can represent each force as a vector in the Cartesian coordinate system, using their magnitudes and angles: F1 = 146 lbs at 295° F2 = 69 lbs at 235° F3 = 140 lbs at 75°
Next, we can find the horizontal and vertical components of each force. The horizontal component (Fx) is calculated as magnitude × cos(angle), and the vertical component (Fy) is magnitude × sin(angle): F1x = 146 lbs × cos(295°) F1y = 146 lbs × sin(295°) F2x = 69 lbs × cos(235°) F2y = 69 lbs × sin(235°) F3x = 140 lbs × cos(75°) F3y = 140 lbs × sin(75°)
Once we have the horizontal and vertical components of each force, we can add them separately to find the total horizontal component (Rx) and total vertical component (Ry): Rx = F1x + F2x + F3x Ry = F1y + F2y + F3y
Finally, we can calculate the magnitude of the resultant force (R) using the Pythagorean theorem: R = sqrt(Rx² + Ry²), and the angle (θ) using the inverse tangent function: θ = atan2(Ry, Rx).
By substituting the values from the given magnitudes and angles, we get resultant force of 89.3lbs at a an angel of 52.6
To know more about resultant force refer:
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