Calculate the net or resultant force in N in x direction given that F1=96.2 N is applied at angle of α=55.4° and a second F2=11.6 N is applied at angle of β=41.2°. See attached figure. Express your answer to 4 significant figures.
F1 + F2 = 96.2N.[55.4o] + 11.6N.[41.2o]
X = 96.2*cos55.4 + 11.6*cos41.2=63.35 N
To calculate the net or resultant force in the x-direction, we need to determine the horizontal components of the given forces. Let's analyze each force separately and find their horizontal components.
Force F1 with a magnitude of 96.2 N and an angle of α = 55.4°:
To find the horizontal component of F1, we multiply the force magnitude by the cosine of the angle:
F1x = 96.2 N * cos(55.4°)
Force F2 with a magnitude of 11.6 N and an angle of β = 41.2°:
To find the horizontal component of F2, we again multiply the force magnitude by the cosine of the angle:
F2x = 11.6 N * cos(41.2°)
Now, we can calculate the net or resultant force in the x-direction by summing up the horizontal components of F1 and F2:
Resultant force in the x-direction, Fx = F1x + F2x
To find the values of cos(55.4°) and cos(41.2°), you can use a scientific calculator or an online tool.
Once you have the values of F1x and F2x, substitute them into the equation for Fx and calculate the result. Round your answer to 4 significant figures as requested.
Keep in mind that if the forces are acting in the opposite direction, you may need to subtract the horizontal components instead of adding.