Normal and Tangential Coordinates

In summary, the question asks for the radius of curvature of a 2-oz bead with an initial speed of 5 ft/sec at point A on a smooth guide that is curved in the horizontal plane. The horizontal force between the bead and the guide has a magnitude of 3 oz at point B. The student is unsure if the force should be in the horizontal or normal direction, but it is clarified that finding the force in the normal direction will also give the force in the horizontal direction.
  • #1
Northbysouth
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Homework Statement


The 2-oz bead P is given an initial speed of 5 ft/sec at point A of the smooth guide which is curved in the horizontal plane. The horizontal force between the bead and the guide has a magnitude of 3 oz at point B.

Determine the radius of curvature ρ of the path at this point


I have attached an image of the question.

Homework Equations





The Attempt at a Solution



The question is fairly straightforward but I'm confused by the 'horizontal force'. My professor went over this example in class and when she drew the FBD she had the 3oz force pointing in the positive normal direction and I'm wondering if she meant for the question to say that the force is in the normal direction instead of in the horizontal direction.

Any insight would be appreciated.
 

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  • #2
Can you see that the "normal direction" is horizontal? So, finding the force in the normal direction will also give the force in the horizontal direction.
 

1. What are normal and tangential coordinates?

Normal and tangential coordinates are a type of coordinate system used in physics and engineering to describe the motion of an object in three-dimensional space. The normal coordinate is perpendicular to the tangent plane of the object's trajectory, while the tangential coordinate is parallel to the tangent plane.

2. How are normal and tangential coordinates related to polar coordinates?

Normal and tangential coordinates are a variation of polar coordinates, where the radius vector is replaced by the normal coordinate and the angle is replaced by the tangential coordinate. This allows for a more precise description of an object's motion, especially in cases where the trajectory is not circular.

3. What is the difference between normal and tangential coordinates?

The main difference between normal and tangential coordinates is their direction. The normal coordinate is perpendicular to the tangent plane and points away from the center of curvature, while the tangential coordinate is parallel to the tangent plane and points in the direction of motion.

4. How are normal and tangential coordinates used in physics?

Normal and tangential coordinates are used in physics to analyze the motion of objects in three-dimensional space. They are particularly useful in cases where the trajectory is not a simple curve, such as in circular motion or projectile motion. They allow for a more accurate and detailed description of an object's motion compared to traditional Cartesian coordinates.

5. Can normal and tangential coordinates be converted to Cartesian coordinates?

Yes, normal and tangential coordinates can be converted to Cartesian coordinates using mathematical equations. This conversion can be useful for simplifying calculations or for plotting the trajectory of an object on a graph. However, it is important to note that the conversion may introduce rounding errors and may not accurately represent the true motion of the object.

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