# Comapring acceleration of person in elevator

• songoku
In summary, when two persons of equal mass stand in identical elevators, with one hanging from the ceiling and the other standing normally, the acceleration experienced by each person will be different in magnitude and direction due to the presence of additional forces acting on the person hanging from the ceiling. However, without knowing the exact values of these forces, the answer cannot be determined and is therefore "not enough information".

## Homework Statement

Two persons, each having mass 70 kg, stand in identical elevators. One stand normally, one hangs in the ceiling of elevator. How is the acceleration of them when the elevators move?

a. Equal in magnitude and direction

b. Equal in magnitude and opposite in direction

c. Different in magnitude but equal in direction

d. Different in magnitude and direction

e. Not enough information

F = m.a

## The Attempt at a Solution

I assume the second person hangs on a rope attached to the ceiling of the elevator so there are two forces acting on the man, weight and tension. There are also two forces acting on the man who stands in the elevator, weight and normal force.

Assuming the elevators move upwards, the acceleration experienced by each man is:

a = (T - W) / m and a = (N - W)/m

We don't know the exact value of T and N, so the answer will be "not enough information"?

Thanks

songoku said:
I assume the second person hangs on a rope attached to the ceiling of the elevator so there are two forces acting on the man, weight and tension. There are also two forces acting on the man who stands in the elevator, weight and normal force.

Assuming the elevators move upwards, the acceleration experienced by each man is:

a = (T - W) / m and a = (N - W)/m

We don't know the exact value of T and N, so the answer will be "not enough information"?
Who says?

T = W + ma

N = W + ma

T = N

Chet

Chestermiller said:
Who says?

T = W + ma

N = W + ma

T = N

Chet

T = N is only when the acceleration of the two elevators is the same. Does the phrase: "identical elevators" imply that those elevators will move with same acceleration or just imply that the elevators have the same mass?

Thanks

songoku said:
T = N is only when the acceleration of the two elevators is the same. Does the phrase: "identical elevators" imply that those elevators will move with same acceleration or just imply that the elevators have the same mass?

Thanks
It's open to interpretation. It doesn't really matter does it? The important thing is that you analyzed the situation correctly.

Chet

It is normal in such introductory problems to make simplifying assumptions such as "identical elevators" => elevators are accelerating at the same rate and in the same gravitational field. That is, the elevators are identical in all respects that are significant to the problem at hand.

OK. Thanks a lot for all the explanation