Calculating the Velocity of an Elevator

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Homework Help Overview

The discussion revolves around a physics problem involving an elevator moving at a constant velocity and the motion of keys released from a height within the elevator. The problem requires calculating the velocity of the elevator and analyzing the height difference when the keys are released while the elevator is moving upwards and then downwards.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between the time the keys are in free fall and the motion of the elevator. Questions arise regarding the assumptions about the elevator's velocity and acceleration, as well as the time it takes for the keys to fall.

Discussion Status

The discussion is ongoing with participants questioning the definitions and assumptions related to the problem. Some guidance has been offered regarding the relationship between the elevator's motion and the keys' trajectory, but no consensus has been reached on the specific calculations or interpretations.

Contextual Notes

There is a focus on the implications of the elevator's constant velocity and the timing of the keys' release. Participants are also considering how the time of the elevator's upward motion relates to the time the keys take to fall, with some uncertainty about the relevance of the 2-second duration mentioned in the problem.

  • #31
mdavies23 said:
v
Can you be a bit clearer? We are now discussing the trajectory of the keys. Of the five variables I listed, acceleration, time, displacement, initial velocity and final velocity you correctly posted that we know the first three: a, t, s. Which velocity do we know?
 
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  • #32
haruspex said:
Can you be a bit clearer? We are now discussing the trajectory of the keys. Of the five variables I listed, acceleration, time, displacement, initial velocity and final velocity you correctly posted that we know the first three: a, t, s. Which velocity do we know?
We know both initial=final
 
  • #33
mdavies23 said:
We know both initial=final
Explain more. What do you think the initial speed is? How do you deduce it is the same as the final?
 
  • #34
haruspex said:
Explain more. What do you think the initial speed is? How do you deduce it is the same as the final?
The initial speed is the same as the elevator and the final speed is also the speed of the elevator
 
  • #35
If I understand where @haruspex is leading you, you can get an equation for key position above the starting point as a function of time, elevator velocity and gravity. You can get a simpler equation for elevator floor position above the starting point as a function of time, elevator velocity and gravity. You can then equate the two and solve for time.

It would seem that a simpler (but arguably equivalent) approach would be to switch for a moment to a reference frame in which the elevator is at rest. Figure out how long the keys take to drop one meter to the floor using this frame. Then switch back to the ground frame.
 
  • #36
mdavies23 said:
The initial speed is the same as the elevator
Yes.
mdavies23 said:
the final speed is also the speed of the elevator
No. This is a common blunder. The equations are for constant acceleration. As soon as the keys touch the ground the acceleration is no longer constant, so the the equations don't apply. We can only apply them up to the instant before they hit the ground, and at that time they will have quite a different velocity from the elevator's.

So we have these four: time, acceleration, initial velocity and displacement. Which SUVAT equation has those four?
 

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