Bolt Falling from elevator ceiling

In summary: Gravity is pulling the bolt downward. So the velocity is positive. And the 3.0m is negative because it's going down.
  • #1

Homework Statement



An elevator ascends with a constant speed of 2.5m/s. A loose bolt drops from the ceiling of the elevator which is 3.0m above the floor.

a) How long does it take the bolt to fall from the ceiling to the floor of the elevator?
b) What are the displacements of the bolt and the elevator floor in this time?


Homework Equations



constant acceleration (with acceleration equal to gravity at 9.81m/s/s)

The Attempt at a Solution



I managed to get the first part, with t = 1.08 s, but now I am confused with part B. I am not sure what the displacement of the elevator floor really is (I cannot picture it) and I assumed the displacement of the bolt at this time was the 3m that it fell (that's the value of displacement I used to get the time in the first place) SO now I am quite confused.

Can anyone give me a hand?
Thanks!
 
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  • #2
cal.queen92 said:

Homework Statement



An elevator ascends with a constant speed of 2.5m/s. A loose bolt drops from the ceiling of the elevator which is 3.0m above the floor.

a) How long does it take the bolt to fall from the ceiling to the floor of the elevator?
b) What are the displacements of the bolt and the elevator floor in this time?


Homework Equations



constant acceleration (with acceleration equal to gravity at 9.81m/s/s)

The Attempt at a Solution



I managed to get the first part, with t = 1.08 s, but now I am confused with part B. I am not sure what the displacement of the elevator floor really is (I cannot picture it) and I assumed the displacement of the bolt at this time was the 3m that it fell (that's the value of displacement I used to get the time in the first place) SO now I am quite confused.

Can anyone give me a hand?
Thanks!
You can do the problem from either frame of reference ( the elevator - or - the building ). They're both inertial frames of reference. But I think the second part of the problem is written with the idea that the building is the frame of reference.

During the time it takes the bolt to fall (1.08s), how far does the floor of the elevator move? - and in what direction?

So, the bolt fell 3m minus the amount the floor moved upward - both in that 1.08 s of time. (BTW: I would expect up to be positive & down to be negative - for your final answers.)

I'll do a follow-up about why you got the right answer for A even though you ignored the displacement of the floor.
 
  • #3
Actually, i don't know if I got the right answer for the time, and if you say I need to consider the displacement of the elevator, I'll try again, though I'm confused now how to find the time it takes for the bolt to hit the ground...
 
  • #4
Take floor as the refeence frame. Then the bolt is moving down wards direction with an initial velocity vo. Then the displacement, initial velocity and g are in the same direction.
Write the proper kinematic equation to solvce for t.
 
  • #5
If you use the elevator as the reference frame, then the displacement of the floor of the elevator is zero. I doubt that the answer key has that.

From the frame of reference of the building, the bolt has the same initial velocity as the elevator.

Let's say the bolt come loose at time t=0, and the position of the floor at that time is: y0. Then the position of the bolt is y0+3.0 at time t=0.

Position of the floor at time t: (Remember, the elevator & its floor have constant velocity v0 = 2.5m/s .)
yfloor = y0 + v0·t .​
Position of the bolt at time t: (The initial velocity of the bolt is also v0=2.5m/s at t=0. This is using the building as the reference frame.)
ybolt = y0 + 3.0 + v0·t ‒ (1/2)g·t2 .​

If you set yfloor = ybolt, and solve for t, you get the time at which the bolt hits the floor. Most everything cancels and you get:

3.0 = (1/2)g·t2, which is the same as if the bolt falls 3.0 m starting at rest.

BTW: I see that your answer to part (a) is incorrect.
 
  • #6
Okay, so to find the time it takes the bolt to fall to the ground I let the equation for the position of the floor equal the equation for the position of the bolt, and I end up with that final, smaller equation.

What I'm confused about is the direction of the velocity, acceleration, and 3.0m. Someone above said they all had the same, however, Would the accleration be negative (gravity pushing down), the velocity be positive (moving up, opposing negative gravity) and the 3.0m be negative since it moves downward, in the same direction as gravity?

That's where I'm getting lost...
 
  • #7
I've drawn a sketch and think I understand now the direction everything is going and have ended up with t=0.78s

I figure, that if I take the acceleration as negative (since it is going down) as well as the 3.0m, then as i work through the equation, I end up with a positive time. (Velocity is positive as it opposes gravity - goes up):

3.0 = (-1/2)g*t^2 --> 3.0 = 4.81*t^2 etc, etc... Is this proper reasoning? Or not logical?
 
  • #8
Now I don't know what the initial y would be? to fill in the equations...
 
  • #9
The initial velocity of the bolt is 2.5 m/s in the upward direction.
After timr t, the bolt reaches the floor of the elevator. Let the bolt covers h1 and floor moves up through h2 during that time. Then
h1 = vo*t - 0.5*g*t^2
h2 = vo*t and h = h1 + h2.
Now solve for t.
 
  • #10
I used the instructions earlier to solve for t and got 0.78s... I think that's right?

Now i can't figure out how to use your equations to solve for time to see if I get he same answer twice. I don't have h1 or h2, and no t, so I am missing some values to solve for t aren't I?

And when I use the result for time I got with the previous equations, I just get 3.0m for the displacement of the bolt... (this is when I subtract the result for h2 from h1 - to take the displacement of the elevator away from that of the bolt)
 
  • #11
I used the instructions earlier to solve for t and got 0.78s... I think that's right?

Now i can't figure out how to use your equations to solve for time to see if I get he same answer twice. I don't have h1 or h2, and no t, so I am missing some values to solve for t aren't I?

And when I use the result for time I got with the previous equations, I just get 3.0m for the displacement of the bolt... (this is when I subtract the result for h2 from h1 - to take the displacement of the elevator away from that of the bolt)
 
  • #12
h1 = vo*t - 0.5*g*t^2...(1)
h2 = vo*t ...(2)
and h = h1 + h2= 3. Add eq.
3 = 2*2.5*t - 0.5*9.8*t^2
Solve for t.
 

1. What causes a bolt to fall from an elevator ceiling?

There could be multiple reasons why a bolt may fall from an elevator ceiling. It could be due to wear and tear over time, improper installation, or vibrations that cause the bolt to become loose.

2. Is it dangerous if a bolt falls from an elevator ceiling?

It depends on the size and weight of the bolt as well as the location where it falls. If the bolt is small and falls in an area where it cannot harm anyone, it may not be dangerous. However, if it falls in a crowded elevator or hits someone, it could potentially cause harm.

3. How can we prevent bolts from falling from elevator ceilings?

Regular maintenance and inspections can help identify any loose or damaged bolts and fix them before they become a safety hazard. It is also important to ensure that bolts are properly installed and secured in the first place.

4. Can a bolt falling from an elevator ceiling indicate a larger problem?

In some cases, a bolt falling from an elevator ceiling may be a sign of a larger issue with the elevator's structural integrity or maintenance. It is important to address the issue promptly to prevent any potential accidents or further damage.

5. What should I do if I see a bolt fall from an elevator ceiling?

If you witness a bolt falling from an elevator ceiling, you should report it to the building management or elevator maintenance team immediately. They will be able to assess the situation and take the necessary steps to ensure the safety of the elevator and its passengers.

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