Relative motion in an elevator

In summary, the conversation discusses the movement of a ball in an elevator and how an observer on the ground would perceive it. The elevator is moving upwards at a rate of 2 m/s while the ball is thrown up and down from a 1 meter distance. It is determined that the observer would see the ball reach a higher height and move a shorter distance on its way down compared to the observer in the elevator. The difference in time between the two perspectives is also explored, with a suggestion to use kinematics to prove the difference. It is noted that the observers would disagree about the vertical speed of the ball at any given instant. Calculations are then presented to determine the time for the ball to rise and fall from both perspectives.
  • #1
Ravens Fan
1
0

Homework Statement


So I am in an elevator throwing a ball in an air, straight up and down, about 1 meter from my hand. The elevator is moving upwards at a rate of 2 m/s. From an observer on the ground, would they see the ball reach its peak at the same instant that I do? If not what is this difference in time.

From my perspective, I see the ball move up 1 meter, then down 1 meter. How far up and down would the observer see the ball move?

2. The attempt at a solution
My thoughts are that the observer would see the ball go higher up, as opposed to 1 m. But then they would see the ball move a shorter distance on the way down. As for the first part, I'm not sure where to begin. My guess is that the times would not be the same, but again, I'm in a stump. Thanks
 
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  • #2
I think you guessed right but maybe you could prove it using kinematics?
 
  • #3
Unless you are considering special relativistic effects, the time would be the same for both observer.
 
  • #4
rpthomps said:
Unless you are considering special relativistic effects, the time would be the same for both observer.
That would be true if they agreed about the event, but as the OP noted, they would disagree about the vertical speed of the ball at any given instant. In particular they would disagree about whether its vertical speed is zero.
 
  • #5
Ravens Fan said:

Homework Statement


So I am in an elevator throwing a ball in an air, straight up and down, about 1 meter from my hand. The elevator is moving upwards at a rate of 2 m/s. From an observer on the ground, would they see the ball reach its peak at the same instant that I do? If not what is this difference in time.

From my perspective, I see the ball move up 1 meter, then down 1 meter. How far up and down would the observer see the ball move?

2. The attempt at a solution
My thoughts are that the observer would see the ball go higher up, as opposed to 1 m. But then they would see the ball move a shorter distance on the way down. As for the first part, I'm not sure where to begin. My guess is that the times would not be the same, but again, I'm in a stump. Thanks
Why don't you do the math, and let the math answer the question for you?

Chet
 
  • #6
haruspex said:
That would be true if they agreed about the event, but as the OP noted, they would disagree about the vertical speed of the ball at any given instant. In particular they would disagree about whether its vertical speed is zero.

I never considered this. It seems quite dramatic. I did some calculations and came up with the following general forms.

From inside the elevator time of object to rise and fall:

##t=\frac { 2v_o}{g }##

From outside the elevator:

##t=\frac{v_o+\sqrt { v_o^2-v_E^2 } +v_E}{g}##

Although I didn't originate the question, I learned a lot. Thanks
 

FAQ: Relative motion in an elevator

What is relative motion in an elevator?

Relative motion in an elevator refers to the perceived movement of objects or individuals inside an elevator in relation to the elevator itself. This can be affected by the motion of the elevator, as well as the frame of reference of the observer.

How does the motion of an elevator affect relative motion?

The motion of an elevator can greatly impact the perceived relative motion of objects or individuals inside. When the elevator is accelerating or decelerating, objects may appear to be moving in the opposite direction due to inertia. Additionally, when the elevator is moving at a constant speed, objects may appear to be stationary.

What is the frame of reference for relative motion in an elevator?

The frame of reference for relative motion in an elevator is the elevator itself. This means that any motion observed by an individual inside the elevator is relative to the elevator's motion, rather than the motion of the surrounding environment.

How does gravity affect relative motion in an elevator?

Gravity plays a significant role in relative motion in an elevator. As the elevator moves up or down, gravity causes objects to experience a change in weight. This can affect the perceived motion of objects inside the elevator.

How does relative motion in an elevator differ from absolute motion?

Relative motion in an elevator is dependent on the motion of the elevator itself, whereas absolute motion is independent of any other frame of reference. This means that absolute motion is not affected by the motion of the elevator, but relative motion is.

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