If theta equals 60 and F equals 450 Newtons, determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis.
2eqwr
hli
force 15i -16j N is added to another 23i N. In what direct measured from the positive x-axis does the resultant act?
To determine the magnitude of the resultant force, we can use the formula:
F_res = F * cos(theta)
where F is the given force magnitude (450 Newtons) and theta is the angle measured counterclockwise from the positive x-axis (60 degrees).
First, convert the angle from degrees to radians:
theta_radians = (60 degrees) * (π/180) radians/degree
Next, substitute the values into the formula:
F_res = (450 Newtons) * cos(60 radians)
Use a calculator to find the cosine of 60 radians (or 60 degrees if your calculator is in degree mode), and multiply it by the given force magnitude to find the magnitude of the resultant force.
To determine the direction of the resultant force, we can use the formula:
θ_res = 180 degrees - theta
where theta is the given angle (60 degrees).
Substitute the value into the formula:
θ_res = 180 degrees - 60 degrees
Simplify using basic arithmetic to determine the angle in degrees counterclockwise from the positive x-axis.
Therefore, to find the magnitude of the resultant force and its direction measured counterclockwise from the positive x-axis, calculate F_res using F * cos(theta) and calculate θ_res using 180 degrees - theta.