Why are there two different equations for normal force on an angle?

Click For Summary

Homework Help Overview

The discussion revolves around the concept of normal force in physics, particularly in scenarios involving inclined planes and banked curves. The original poster expresses confusion regarding two different equations for normal force: one being Fn = mg cos(θ) and the other Fn = mg / cos(θ), questioning how the choice of coordinate axes affects these equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definitions and applications of normal force in different contexts, such as sliding on a slope versus a car navigating a banked curve. Questions arise about the implications of changing coordinate systems and how this affects the interpretation of forces involved.

Discussion Status

Some participants have provided insights into the conditions under which each equation applies, noting that the normal force can vary based on additional forces acting on the object. The discussion is ongoing, with participants seeking to clarify their understanding of the underlying principles.

Contextual Notes

The original poster mentions a potential misunderstanding stemming from high school versus university-level physics, indicating a shift in how normal force is conceptualized in different scenarios. There is also a reference to the importance of visual aids, such as drawings, to better understand the relationships between forces.

student34
Messages
639
Reaction score
21

Homework Statement



I feel like I am being told that there two different kinds of normal force.

1st. In grade 11 we were always told that normal force on an angle equals m*g*cosθ, where Fn equals the y-component, and θ is the angle between Fn and mg.

2nd. Now in university we are told that the normal force can also equal (m*g)/cosθ, where θ is still the angle between Fn and mg, but mg is the y-component and Fn is the hypontuse.

What is going on? The only difference that I see is changes to what the x and y axises are. Why does changing the x and y axises change the ratio of Fn and mg?
 
Physics news on Phys.org
Normal force is a force of constraint, it keeps the object moving on the constrained path. It depends on the situation. When an object slides along a slope, with only gravity acting on it, the normal force is Fn=mgcos(θ) where θ is the angle of inclination (also the angle of the normal with respect to the vertical).

What was the other problem? If there are other forces, the normal force can be different. For example, if the object on the slop is pressed against the slope by some force F, and it is stationary, the normal force is mg/cos(θ)

ehild
 
ehild said:
Normal force is a force of constraint, it keeps the object moving on the constrained path. It depends on the situation. When an object slides along a slope, with only gravity acting on it, the normal force is Fn=mgcos(θ) where θ is the angle of inclination (also the angle of the normal with respect to the vertical).

What was the other problem? If there are other forces, the normal force can be different. For example, if the object on the slop is pressed against the slope by some force F, and it is stationary, the normal force is mg/cos(θ)

ehild

Yes, the 2nd normal force where normal force is mg/cos(θ) is about a car taking a banked corner. I am really confused. Why does this problem make Fn the hypotnuse and mg the vertical component? And why do we change x and y axises to do it?
 
A drawing always helps.The car drives along a horizontal circle. That means the net force acting on it is horizontal, and equal to the centripetal force, Fcp. Gravity is vertical so the centripetal force is provided by the horizontal component of the normal force while the vertical component balances the weight of the car. If you add the vectors W and N you get a horizontal vector. See the yellow triangle: N is the hypotenuse.

ehild
 

Attachments

  • bankroad.JPG
    bankroad.JPG
    6.6 KB · Views: 490
ehild said:
A drawing always helps.The car drives along a horizontal circle. That means the net force acting on it is horizontal, and equal to the centripetal force, Fcp. Gravity is vertical so the centripetal force is provided by the horizontal component of the normal force while the vertical component balances the weight of the car. If you add the vectors W and N you get a horizontal vector. See the yellow triangle: N is the hypotenuse.

ehild

Ah, I get it, thanks.
 
You are welcome. Do not forget to draw next time:-p

ehild
 

Similar threads

  • · Replies 20 ·
Replies
20
Views
2K
Replies
2
Views
2K
  • · Replies 18 ·
Replies
18
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K