A force directed 47.5° below the positive x-axis has an x component of 5.09 lb. Find its y component.
y / x = tan(-47.5º)
y = x * tan(-47.5º)
To find the y component of the force, we can use trigonometry. The given angle is 47.5° below the positive x-axis, which means the angle is measured from the negative y-axis.
First, let's define the given information:
Angle: θ = 47.5°
x-component of the force: Fx = 5.09 lb
We can use the following trigonometric relationships:
sin(θ) = Opposite / Hypotenuse
cos(θ) = Adjacent / Hypotenuse
In this case, we are looking for the y-component, which is the opposite side of the angle. So, we'll use the sine function:
sin(θ) = Opposite / Hypotenuse
Rearranging the formula, we have:
Opposite = sin(θ) * Hypotenuse
Now, let's calculate the y-component:
sin(47.5°) = Opposite / Hypotenuse
Since the hypotenuse is not given, we can assume its value to be 1 (it can be any value, as long as it is nonzero).
sin(47.5°) = Opposite / 1
Therefore, Opposite = sin(47.5°), which gives us the y-component of the force.
Let's calculate:
Opposite = sin(47.5°) = 0.7312
Hence, the y-component of the force is approximately 0.7312 lb.