How Do You Solve for Normal Force in Different Dynamics?

[Impulse]

Homework Statement

The problem motivating this post is: "An out-of-gas car is rolling over the top of a hill at speed v. At this instant,
a. n > F_G
b. n < F_G
c. n = F_G
d. We can't tell about n without knowing v." (Associated figure attached.)

Homework Equations

[/B]
Newton's second law

The Attempt at a Solution

What I'd like to understand is in what framework to think about the normal force.

I currently understand the normal force to be equal and opposite to the perpendicular force exerted by an object on the surface with which it is in contact. I still believe this to be correct.

I'm wrestling with how to solve for the normal force. Originally, I assumed it was always equal and opposite to the perpendicular component of the force of gravity, such as is the case in a standard incline plane problem. To solve for the normal force, I would first solve for the perpendicular component of the force of gravity, then flip the sign. However, the motivating problem I posted above, as well as examining a car doing a vertical loop-the-loop and driving around a curve on a banked track, has shown that this framework for solving for the normal force can be faulty.

It now appears that, to solve for the normal force acting on an object, I should first determine the resulting motion of the object known to be true in a given scenario and then set the normal force equal to whatever force is required to make that motion result. So, in the motivating problem above, because I know the car will roll down the other side of the hill, the downward force of gravity must exceed the upward normal force, and the answer must be "b".

Is this line of thinking how you understand to solve for the normal force?

The paradigm of "first determine how you know the system to act, then set a force equal to whatever is required to make the system act in that way" feels foreign to me. I'm used to "first solve for all the forces, then determine how the system will act as a result of those forces."

 

[Chestermiller]

Is the direction of the car's velocity vector constant as the car goes over the hill, or is it changing? What does this tell you about the car's acceleration? What does that tell you about the net force acting on the car?

Chet

 

[OldEngr63]

What normal force did you have in mind?

There is the normal force between the wheel and the road;
the normal force between the air and the car;
the normal force between the axle and the car body,
etc.

 

[BvU]

@Old: come on, a clear picture is provided !

@IMP: Chet's chat makes good sense to me !

 

[HalfLostAndSearching]

As a scientist, it is important to approach problems and concepts with an open mind and a willingness to adapt to new information and perspectives. In the case of the normal force, it is important to understand that it is not always equal and opposite to the perpendicular component of the force of gravity, as you have discovered with the examples you provided.

Your understanding of the normal force as being equal and opposite to the perpendicular force exerted by an object on the surface it is in contact with is correct. However, as you have observed, this may not always be a helpful framework for solving for the normal force.

In some cases, it may be more useful to approach the problem by first determining the motion of the object and then setting the normal force equal to whatever force is required to make that motion occur. This may involve considering other forces acting on the object, such as friction or centripetal force, in addition to the force of gravity.

Ultimately, the key is to approach each problem by carefully considering all the forces acting on the object and using the appropriate framework or approach to solve for the normal force. This may involve using Newton's second law or other relevant equations.

In summary, it is important to have a solid understanding of the concept of the normal force, but also to be flexible in your approach to solving problems involving it. As a scientist, it is important to constantly evaluate and adapt your understanding and problem-solving strategies based on new information and perspectives.