Is the Normal Force in an Elevator Conservative?

In summary, we can conclude that the normal force is not conservative because there is at least one case, like this, in which in a closed trajectory the total work is not zero. This is shown in the example of a person stepping into an elevator and traveling to different floors, where their kinetic energy and the total work done on them by the elevator is not zero. Therefore, the normal force cannot be considered a conservative force.
  • #1
Caio Graco
40
2
Homework Statement
Can normal force work? If so, is it a conservative force?
Relevant Equations
There is no equation for normal force.
Consider a body inside an elevator. When it goes up and down, I believe that normal work (positive on the rise and negative on the descent). My question is: since the total work on the closed path is zero, can we say that the normal force is conservative?
 
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  • #2
Caio Graco said:
Consider a body inside an elevator. When it goes up and down, I believe that normal work (positive on the rise and negative on the descent).
Simply not true. When accelerating down the elevator exerts a normal force that is still "up" (not negative) and large enough so that your acceleration matches the elevator's acceleration. If that were not the case, you would either hit the roof or, even worse, fall through the floor.

You need to think what the criterion for a conservative force is.
 
  • #3
Caio Graco said:
Consider a body inside an elevator. When it goes up and down, I believe that normal work (positive on the rise and negative on the descent). My question is: since the total work on the closed path is zero, can we say that the normal force is conservative?
Suppose that you step into the elevator on the 2nd floor. The elevator is at rest. Your kinetic energy is zero.

You press the button labelled "3" and rise to the third floor. The elevator stops here. You press the button labelled "1" (or "G"). The elevator proceeds downward past the 2nd floor without stopping.

At the moment that the elevator passes the second floor is your kinetic energy greater than, less than or equal to what it was when you first pressed the "3" button? At this moment, is is the total work that has been done on you by the elevator positive, negative or zero?
 
  • #4
jbriggs444 said:
Suppose that you step into the elevator on the 2nd floor. The elevator is at rest. Your kinetic energy is zero.

You press the button labelled "3" and rise to the third floor. The elevator stops here. You press the button labelled "1" (or "G"). The elevator proceeds downward past the 2nd floor without stopping.

At the moment that the elevator passes the second floor is your kinetic energy greater than, less than or equal to what it was when you first pressed the "3" button? At this moment, is is the total work that has been done on you by the elevator positive, negative or zero?

By the time the elevator passes the second floor, my kinetic energy is greater than it was at the beginning. So the total work on me is positive. And I believe this shows that the normal force is not conservative because there is at least one case, like this, in which in a closed trajectory the total work is not zero. Is this friend?
 
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  • #5
Caio Graco said:
the normal force is not conservative because there is at least one case, like this, in which in a closed trajectory the total work is not zero
Yes.
 
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Related to Is the Normal Force in an Elevator Conservative?

1. How does normal force change in an elevator?

The normal force in an elevator changes depending on the direction of the elevator's motion. When the elevator is at rest or moving at a constant velocity, the normal force is equal to the weight of the object inside the elevator. However, when the elevator accelerates upwards or downwards, the normal force increases or decreases, respectively.

2. Why is normal force important in an elevator?

Normal force is important in an elevator because it is responsible for supporting the weight of objects and people inside the elevator. Without the normal force, the objects would fall to the ground due to the force of gravity. Additionally, the normal force helps to maintain the structural integrity of the elevator by balancing the weight load.

3. How does the normal force affect the feeling of weightlessness in an elevator?

The normal force is essential in creating the feeling of weightlessness in an elevator. When an elevator is in free fall, the normal force decreases to zero, resulting in a feeling of weightlessness for the objects and people inside. This is because there is no contact force between the elevator and the objects, allowing them to fall together at the same rate.

4. Does the normal force change if the elevator is on an inclined surface?

Yes, the normal force changes when an elevator is on an inclined surface. The normal force is now divided into two components: one perpendicular to the surface (perpendicular to the weight) and one parallel to the surface (frictional force). The normal force perpendicular to the surface is equal to the weight, while the normal force parallel to the surface is equal to the frictional force needed to keep the elevator from sliding down the incline.

5. How can the normal force be calculated in an elevator?

The normal force can be calculated by using the equation: FN = mg + ma, where FN is the normal force, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the elevator. This equation takes into account the weight of the object and the additional force exerted by the elevator's acceleration.

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