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What happens to forces as the incline increases? Weight (F W) stays the same; Normal force (F N) decreases; Parallel force (F ⸗) increases
11 Αυγ 2021 · Since only the normal force n and one component of the weight w acts along this direction, then we get: ∑F = 0 ⇔ n − w ⊥ = 0 ⇔ n = w ⊥. Now you just need to find the perpendicular component of the weight. That turns out to include the cosine of the angle due to trigonometry: w ⊥ = mgcos(α).
Normal Force: Remember that a normal force F N is always perpendicular to the surface that you are on. Since this surface is slanted at a bit of an angle, the normal force will also point at a bit of an angle.
The normal force is always perpendicular to the surface, and since there is no motion perpendicular to the surface, the normal force should equal the component of the skier’s weight perpendicular to the slope.
for the direction perpendicular to the plane. Of course, since there is no motion in this direction, \(a_y\) is zero. This gives us immediately the value of the normal force: \[ F^{n}=F^{g} \cos \theta=m g \cos \theta \label{eq:8.17} \] since \(F^g = mg\).
The normal force must always be perpendicular to the surface. However, when the surface is inclined, the normal force is not equal to the gravitational force, but rather to the component of the gravitational force that is perpendicular to the surface (shown in blue in the diagram below).
Force and Motion on an Incline. An inclined plane is basically a ramp. It is a flat surface that is sloped rather than horizontal. When solving problems about objects on an incline, it is convenient to choose a coordinate system with axes parallel and perpendicular to the surface as shown in Fig. 1. +y.
