Relationship between angle of banked road and normal force and its component

Question

Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.

This is a plane geometry problem. – user45664 Mar 11 '19 at 20:17 — user45664, Mar 11 '19 at 20:17

Steeven · Accepted Answer · 2019-03-12T08:32:49.927

2

On flat ground, $N$ points straight up.

Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $\theta$, and $N$ must as well tilt with $\theta$ in the same rotational direction (clockwise in your case).

Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.

edited Mar 12 '19 at 08:32

answered Mar 11 '19 at 10:40

Steeven

749

score 1 · Answer 2 · answered Mar 12 '19 at 08:43

1

The angle between $f$ and the $x$-axis is equal to $\theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $\theta$ because alternate interior angles are equal.

answered Mar 12 '19 at 08:43

John Douma

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Relationship between angle of banked road and normal force and its component

2 Answers2