A force vector has a magnitude of 576 newtons and points at an angle 43o of below the positive x axis. What are (a) the x scalar component and (b) the y scalar component of the vector?
This is a matter of resolving a vector into components. Basic stuff.
a) 576 cos 43
b) 576 sin (-43)
assuming the +x axis is up.
To find the x and y scalar components of a force vector, we can use trigonometry.
First, let's visualize the given information. The force vector is pointing at an angle of 43° below the positive x-axis.
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43°
The magnitude of the force vector is given as 576 newtons.
(a) To find the x scalar component, we need to determine the horizontal projection of the force vector. This can be calculated using the cosine function:
x_scalar = magnitude * cos(angle)
In this case, the angle is below the positive x-axis, so we need to consider the negative y-axis direction when calculating the x scalar component. Therefore, the equation becomes:
x_scalar = magnitude * cos(angle)
x_scalar = 576 newtons * cos(43°)
(b) To find the y scalar component, we need to determine the vertical projection of the force vector. This can be calculated using the sine function:
y_scalar = magnitude * sin(angle)
In this case, the angle is below the positive x-axis, so we need to consider the negative y-axis direction when calculating the y scalar component. Therefore, the equation becomes:
y_scalar = magnitude * sin(angle)
y_scalar = 576 newtons * sin(43°)
Now, let's calculate the values for (a) the x scalar component and (b) the y scalar component.