Are the Equations for Normal Force on an Inclined Plane the Same?

In summary, when finding the normal force on an inclined plane, one can use the y-component of the gravity vector and find the components of the normal force to get two different equations. However, these equations are only the same when the object is accelerating along the incline. If the object is moving perpendicular to the plane, the equations will be different.
  • #1
Gear300
1,213
9

Homework Statement


I was doing a problem with normal force on an inclined plane and found the normal force by finding the y-component of the gravity vector. Then I also found that if I find the components of the normal force, I can also get another answer.
-How are the 2 different equations available for the normal force the same


Homework Equations


Fg = mg
Fgy = -mgcos(theta)

Fny = Fncos(theta)


The Attempt at a Solution


Fgy = -mgcos(theta)
Fn - mgcos(theta) = 0 'movement along plane; not vertically
Fn = mgcos(theta)

Fny = Fncos(theta)
Fncos(theta) - mg = 0 'movement along plane; not vertically
Fn = mg/cos(theta)

I got 2 equations for Fn; Fn = mgcos(theta), Fn = mg/cos(theta)...I'm not understanding how the 2 are the same; can anyone help
 
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  • #2
The object is accelerating, [tex]a[/tex], along the direction of the incline.

This means that in a direction perpendicular to the incline it is not accelerating as you correctly assumed in the derivation of your first formula.

One can decompose the acceleration along the incline into x- and y- components though. This means that in the x and y direction one cannot assume that the acceleration of the object is zero. So your second formula is invalid.
 
  • #3
I see; thanks. But, in that case, the second equation would work if let's say the object was moving perpendicular to the plane (such as a car on a banked road), right?
 
  • #4
Yes, because the resultant acceleration is horizontal and there is then no vertical accelleration component.
 
  • #5
Alright; thanks
 

1. What is normal force?

Normal force is the force that a surface exerts on an object that is in contact with it. It is always perpendicular to the surface and acts in the direction opposite to the force applied on the object.

2. What causes normal force?

Normal force is caused by the electromagnetic interactions between molecules in the surface and the molecules of the object in contact with it. These interactions create a repulsive force that balances out the weight of the object.

3. How is normal force different from other forces?

Normal force is different from other forces because it is a reaction force. It only exists when an object is in contact with a surface and is always perpendicular to the surface. Other forces, such as gravity and friction, can act in any direction.

4. How is normal force calculated?

The normal force is calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2). This gives the weight of the object, which is equal to the normal force in the absence of other forces.

5. Can normal force be negative?

No, normal force cannot be negative. It is always directed away from the surface and acts to support the weight of an object. However, it can be zero if there is no contact between the object and the surface, or if the object is in a state of free fall.

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