two forces act on a point object as follows:100N at 170 and 100n at 50
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Am stuck on how the cosins and sins come in. And also how you arrived at 100N at 110°
To solve this problem, we need to find the resultant of the two forces acting at different angles. Here's how we can do it:
1. Break the forces into their horizontal (x) and vertical (y) components using trigonometry.
Force 1:
Magnitude = 100 N
Angle = 170 degrees
Vertical component (F1y) = 100 N * sin(170) ≈ 92.97 N (taking the positive direction as up)
Horizontal component (F1x) = 100 N * cos(170) ≈ -12.93 N (taking the positive direction as right)
Force 2:
Magnitude = 100 N
Angle = 50 degrees
Vertical component (F2y) = 100 N * sin(50) ≈ 76.60 N (taking the positive direction as up)
Horizontal component (F2x) = 100 N * cos(50) ≈ 64.28 N (taking the positive direction as right)
2. Find the resultant components by adding the corresponding x and y components.
Resultant vertical component (Ry) = F1y + F2y = 92.97 N + 76.60 N ≈ 169.57 N (upward direction)
Resultant horizontal component (Rx) = F1x + F2x = -12.93 N + 64.28 N ≈ 51.35 N (rightward direction)
3. Calculate the magnitude and direction of the resultant force using the resultant components.
Resultant magnitude (R) = sqrt(Rx^2 + Ry^2) ≈ sqrt(51.35 N^2 + 169.57 N^2) ≈ 178.55 N
Resultant angle (θ) = arctan(Ry/Rx) = arctan(169.57 N/51.35 N) ≈ 73.70 degrees (measured counterclockwise from the positive x-axis direction)
Therefore, the resultant force acting on the point object is approximately 178.55 N at an angle of 73.70 degrees (counterclockwise from the positive x-axis direction).