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Primary SchoolPhysics 5 points

A force of 10n resolved into perpendicular components if the first components makes 30 with force the magntudes of components

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To find the magnitudes of the components of a force that has been resolved into perpendicular components, we can use trigonometry.

Let's label the force as F, and the magnitudes of the components as Fx and Fy. The angle between the first component and the force is given as 30 degrees.

We know that the total force, F, can be calculated by using the Pythagorean theorem:
F^2 = Fx^2 + Fy^2

Since the force is given as 10N, we can substitute it into the equation:
10^2 = Fx^2 + Fy^2

Next, we'll use trigonometry to find the relationship between the components and the force. The angle between the first component and the force is given as 30 degrees, which means that the cosine of that angle (cos(30°)) relates the adjacent side (Fx) to the hypotenuse (F).

So we can write:
Fx = F * cos(30°)

To find Fy, we'll use the sine of the angle (sin(30°)):
Fy = F * sin(30°)

Now, we can substitute these equations into the first equation to solve for Fx and Fy:
10^2 = (F * cos(30°))^2 + (F * sin(30°))^2

Simplifying the equation:
100 = F^2 * (cos^2(30°) + sin^2(30°))

Since cos^2(30°) + sin^2(30°) equals 1 (due to the trigonometric identity), we can simplify the equation further:
100 = F^2 * 1

Finally, we can solve for F, the magnitude of the force:
F = sqrt(100) = 10N

Therefore, the magnitudes of the components are:
Fx = F * cos(30°) = 10 * cos(30°)
Fy = F * sin(30°) = 10 * sin(30°)