Calculating Time of Fall: Elevator Problem

[Prathamesh]

Homework Statement

An elevator is ascending with a uniform velocity 2 m/s when a loose bolt gets detached from the ceiling and falls on the floor. If the ceiling is 3 m above the floor , find the time required by the bolt to fall from the ceiling to the floor? (g=10 m/s²)

Homework Equations

The Attempt at a Solution

Relative velocity of bolt with respect to floor before detaching=0 m/s Hence u = 0 m/s
So ,
s=ut + 1/2 at²
=1/2 gt²
Hence , t=0.77 s
but solution says that
put u= -2 m/s
Why this is so??

 

[NascentOxygen]

Perhaps the textbook is solving this from the viewpoint of motion relative to the building, i.e., relative to the building's basement?

 

[cnh1995]

Homework Statement

An elevator is ascending with a uniform velocity 2 m/s when a loose bolt gets detached from the ceiling and falls on the floor. If the ceiling is 3 m above the floor , find the time required by the bolt to fall from the ceiling to the floor? (g=10 m/s²)

Homework Equations

The Attempt at a Solution

Relative velocity of bolt with respect to floor before detaching=0 m/s Hence u = 0 m/s
So ,
s=ut + 1/2 at²
=1/2 gt²
Hence , t=0.77 s
but solution says that
put u= -2 m/s
Why this is so??

The bolt had an upward initial velocity, while the displacement is in the downward direction.

 

[haruspex]

Homework Statement

An elevator is ascending with a uniform velocity 2 m/s when a loose bolt gets detached from the ceiling and falls on the floor. If the ceiling is 3 m above the floor , find the time required by the bolt to fall from the ceiling to the floor? (g=10 m/s²)

Homework Equations

The Attempt at a Solution

Relative velocity of bolt with respect to floor before detaching=0 m/s Hence u = 0 m/s
So ,
s=ut + 1/2 at²
=1/2 gt²
Hence , t=0.77 s
but solution says that
put u= -2 m/s
Why this is so??

It's perfectly valid and preferable to use the frame of reference of the lift, as you did. Using the ground frame makes u=-2ms/s, but then the rest of the problem gets messier because you have to take into account the moving floor. If the textbook gets a different answer it is wrong.

 

[Ray Vickson]

Homework Statement

An elevator is ascending with a uniform velocity 2 m/s when a loose bolt gets detached from the ceiling and falls on the floor. If the ceiling is 3 m above the floor , find the time required by the bolt to fall from the ceiling to the floor? (g=10 m/s²)

Homework Equations

The Attempt at a Solution

Relative velocity of bolt with respect to floor before detaching=0 m/s Hence u = 0 m/s
So ,
s=ut + 1/2 at²
=1/2 gt²
Hence , t=0.77 s
but solution says that
put u= -2 m/s
Why this is so??

Since the velocity of the elevator is constant, all laws of Physics (and of mechanics, in particular) are the same as if the elevator were not moving at all! In other words, from the point-of-view of measurements made inside the elevator, you cannot tell if it is moving or stationary. Therefore, you can neglect the elevator's motion in this question, and treat it as a simple problem of a bolt falling from ceiling to floor in your bedroom.

For more on that "not moving" analogy, see, eg.,
http://psi.phys.wits.ac.za/teaching/Connell/phys284/2005/lecture-01/lecture_01/node5.html
which concerns the so-called Galilean invariance of mechanical laws.

 

[haruspex]

Since the velocity of the elevator is constant, all laws of Physics (and of mechanics, in particular) are the same as if the elevator were not moving at all! In other words, from the point-of-view of measurements made inside the elevator, you cannot tell if it is moving or stationary. Therefore, you can neglect the elevator's motion in this question, and treat it as a simple problem of a bolt falling from ceiling to floor in your bedroom.

As I read the OP, that's what Prathamesh did. He asks why the book didn't. What is not clear is whether the book arrived at a different answer.

 

[Prathamesh]

Thank you very much haruspex and ray vickson...
I just wanted to make sure that i m going in r8 direction