Why Is Normal Force Less Than mg at the Top of a Hill?

[corey2014]

So in class today we were talking about Normal Force, and I was really confused on one diagram.

Here is a link about the question, but I don't understand why n<mg because if it is less than mg wouldn't that make it go through the earth? not sure but help understanding would be great thanks!

http://www.colorado.edu/physics/phys1110/phys1110_sm11/ConceptTests/pdf/Lecture6_Using%20Newton_FreeBodyDiagrams_Normal_tension_gravity.pdf

And if the link doesn't work the question is, a car traveling at a constant speed goes over a hill, at the top of the hill what is the normal force?

Thanks for the help!

 

[Doc Al]

Here is a link about the question, but I don't understand why n<mg because if it is less than mg wouldn't that make it go through the earth? not sure but help understanding would be great thanks!

The normal force would equal mg (at least on a horizontal surface) if there were no acceleration normal to the surface the surface. But if there's acceleration in the direction of the surface, the normal force can be less than or greater than mg. Think of an elevator. When the elevator accelerates upward, the normal force from the floor of the elevator on you is greater than your weight.

And if the link doesn't work the question is, a car traveling at a constant speed goes over a hill, at the top of the hill what is the normal force?

When the car travels over a hill, it's actually accelerating. (Think of it as moving in a circle.) So ƩF = ma, thus weight - normal force = ma. So normal force = weight - ma. (You can plug in the value of the centripetal acceleration for a.)

 

[Lsos]

Here is a link about the question, but I don't understand why n<mg because if it is less than mg wouldn't that make it go through the earth?

Why would it go through the earth? The car going over the hill actually tends to go AWAY from the earth. You know how in movies if the car goes fast enough, it actually jumps off the end of the hill? Well in that situation, the normal force would be 0 (or even upwards).

Think of the normal force as what the reading would be if you placed a scale underneath the car. Since the car would be in the air, it wouldn't even be touching the scale.

 

[sophiecentaur]

When the car is going over the hill it is NOT in equilibrium, is it? So you can't insist on using an equilibrium equation to describe what's going on.

 

[PJC01]

Hello,

Acceleration and normal force are two important concepts in physics that are closely related. Acceleration is the rate of change of an object's velocity, while normal force is the force that a surface exerts on an object in contact with it. In the context of your question, normal force is the force that the ground (or surface) exerts on the car as it travels over the hill.

In the diagram you provided, the normal force (n) is shown to be less than the weight of the car (mg). This is because the car is moving in a circular motion, and according to Newton's first law of motion, an object in motion will continue in a straight line at a constant speed unless acted upon by an external force. In this case, the car's motion is being changed by the force of gravity pulling it down towards the center of the circular path. The normal force is the force that balances out this downward pull and keeps the car from falling through the surface.

To answer the question about the normal force at the top of the hill, we need to consider the forces acting on the car. At the top of the hill, the car is still moving in a circular path, so the force of gravity is still pulling it down towards the center of the circle. The normal force is now pointing upwards, and it must be equal in magnitude to the force of gravity in order to keep the car moving in a circular path. Therefore, the normal force at the top of the hill is equal to the weight of the car, or mg.

I hope this helps to clarify the concept of acceleration and normal force for you. It's important to remember that these forces are always working together to keep objects in motion, and that they can change depending on the situation. Keep asking questions and seeking understanding, and you will continue to learn and grow as a scientist.