Forces of 20 N at 80 degrees, and 50 N at an angle of 210 degrees, measured counter-clockwise from the positive x-axis, act on an object.
What are the components (Fx, Fy) of the resultant force (in Newtons)?
To find the components (Fx, Fy) of the resultant force, we need to break down each of the given forces into their x-axis and y-axis components.
For the force of 20 N at 80 degrees, the x-axis component (Fx1) can be found using cosine of the angle:
Fx1 = 20 N * cos(80 degrees)
Similarly, the y-axis component (Fy1) can be found using sine of the angle:
Fy1 = 20 N * sin(80 degrees)
For the force of 50 N at 210 degrees, since the angle is measured counter-clockwise from the positive x-axis, we need to convert the angle to a standard angle measured clockwise from the positive x-axis. We can do this by adding 360 degrees to the angle:
Converted angle = 210 degrees + 360 degrees = 570 degrees
Now, we can find the x-axis component (Fx2) and y-axis component (Fy2) of the force using cosine and sine of the converted angle:
Fx2 = 50 N * cos(570 degrees)
Fy2 = 50 N * sin(570 degrees)
Finally, to find the components (Fx, Fy) of the resultant force, we add up the x-axis components and the y-axis components of both forces:
Fx = Fx1 + Fx2
Fy = Fy1 + Fy2
Plug in the respective values and calculate to find the components of the resultant force in Newtons.
To find the components Fx and Fy of the resultant force, we can use the given magnitudes and angles of the individual forces.
For the force of 20 N at 80 degrees:
Fx = 20 N * cos(80 degrees)
≈ 20 N * (-0.1736)
≈ -3.47 N (rounded to two decimal places)
Fy = 20 N * sin(80 degrees)
≈ 20 N * (0.9848)
≈ 19.70 N (rounded to two decimal places)
For the force of 50 N at 210 degrees:
Fx = 50 N * cos(210 degrees)
≈ 50 N * (-0.8660)
≈ -43.30 N (rounded to two decimal places)
Fy = 50 N * sin(210 degrees)
≈ 50 N * (-0.5000)
≈ -25.00 N
Now we can find the components (Fx, Fy) of the resultant force by summing the respective components of the individual forces:
Fx = -3.47 N + (-43.30 N)
≈ -46.77 N (rounded to two decimal places)
Fy = 19.70 N + (-25.00 N)
≈ -5.30 N (rounded to two decimal places)
Therefore, the components (Fx, Fy) of the resultant force are approximately (-46.77 N, -5.30 N).