Does the elevator speed going up effect the free fall time?

In summary: If the elevator is moving upward with speed (say) v0, then, until it actually comes loose and starts to fall the screw is also moving upward at that speed. That will be the initial speed when it starts to fall. Take the time at which the screw starts to fall to be 0. As soon as the screw comes loose, it starts to accelerate (downward) with acceleration -g. At time t after coming loose, it has speed -gt+ v0. If we take the position of the base of the elevator at t=0 to be 0 and the elevator has height h, then the intial position of the screw is h so the position of the screw at any time
  • #1
Physicsisfun2005
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I ran across this physics problem in class yesterday, it seems simple but...... (assume simplest case) ok...a screw at the top of an elevator that is traveling upwards comes loose and falls. Does the elevator speed going up effect the free fall time? (like does the elevator move toward the screw?) If the elevator is 2.5m tall and is not moving i figure free fall is .714 sec. (h=.5gt^2), is it the same time say if the elevator it traveling at 5 m/s?
 
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  • #2
Assuming the elevator is moving uniformly, its speed won't affect the time the screw takes to fall. If you didn't know the elevator were moving, you would not be able to tell by any mechanical experiment done within the elevator. This is called the principle of Galilean relativity.
 
  • #3
thank you
 
  • #4
Doc Al gave the simplest answer. Here's the more complicated, detailed answer:

If the elevator is moving upward with speed (say) v0, then, until it actually comes loose and starts to fall the screw is also moving upward at that speed. That will be the initial speed when it starts to fall. Take the time at which the screw starts to fall to be 0. As soon as the screw comes loose, it starts to accelerate (downward) with acceleration -g. At time t after coming loose, it has speed -gt+ v0. If we take the position of the base of the elevator at t=0 to be 0 and the elevator has height h, then the intial position of the screw is h so the position of the screw at any time t is -(g/2)t2+ v0t+ h. The position of the bottom of the elevator is v0t. The screw hits the floor when -(g/2)t2+ v0t+h= v0t. The point is that the two "v0t" terms cancel so the speed of the elevator, v0, is irrelevant.
 
  • #5
Relative to the ground "the bottom of the shaft" the screw will fall at a constant rate regardless of elevator speed.
Relative to the floor of the ascending elavator, however, the situation is much different from an occupants viewers point. The rate of the screws' acceleration is the same, but the time for point of impact with the floor is reduced.
 
  • #6
Originally posted by pallidin
Relative to the ground "the bottom of the shaft" the screw will fall at a constant rate regardless of elevator speed.
I don't understand this statement. If you are talking about the speed of the screw with respect to the ground, its speed is V0-gt (as Halls explained). V0 is the speed of the elevator (and thus the initial speed of the screw) so the speed of the screw (with respect to the ground) does depend on the speed of the elevator.
Relative to the floor of the ascending elavator, however, the situation is much different from an occupants viewers point. The rate of the screws' acceleration is the same, but the time for point of impact with the floor is reduced.
Another puzzling statement. An observer on the ground and an observer in the elevator will both agree on the time it takes for the screw to fall to the floor of the elevator.
 
  • #7
Doc,

I see I managed to confuse myself. Thanks for your corrections.

Pallidin
 

1. How does the speed of the elevator affect its free fall time?

The speed of the elevator does not affect its free fall time. The free fall time is determined by the force of gravity, which is a constant. As long as the elevator is in free fall, it will take the same amount of time to reach the ground regardless of its initial speed.

2. Does the weight of the elevator affect its free fall time?

No, the weight of the elevator does not affect its free fall time. The free fall time is determined by the force of gravity, which is independent of an object's weight. This means that all objects, regardless of their weight, will fall at the same rate in a vacuum.

3. What factors do affect the free fall time of an elevator?

The only factor that affects the free fall time of an elevator is the force of gravity. However, external factors such as air resistance or friction may affect the elevator's speed and therefore its overall journey time.

4. Is the free fall time of an elevator different going up compared to going down?

No, the free fall time is the same for both directions. This is because the elevator is still subject to the force of gravity in both cases. The only difference may be in the overall journey time, as the elevator may have a different initial speed or may encounter external factors such as air resistance or friction when going up compared to going down.

5. How can the free fall time of an elevator be calculated?

The free fall time of an elevator can be calculated using the formula t = √(2h/g), where t is the time, h is the height of the elevator, and g is the acceleration due to gravity (9.8 m/s²). This formula assumes that the elevator is in free fall and there are no external factors affecting its speed.

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