Tension on Rope in Elevator: Find the Right Formula

[Viraam]

When the lift accelerates upwards with an acceleration of $a$ then Tension $T$ is given by $m (g+a)$.
In this case should the acceleration due gravity be taken as negative that is $-9.8$ . No right.

 

[Viraam]

Viraam:

If you had drawn a free body diagram for the elevator, you would not be experiencing all this uncertainty. Draw one, and you will see what I mean.

Chet

Thanks, I got it.

 

[NickAtNight]

$T = m (g-a) \\T= m (9.8-9.8) = 0$
Please correct me

That is correct.

1) The tension in the cable can only go to 0. If we want the elevator to go down faster, we would have to attach a cable to the bottom of the elevator and pull it. With no tension, the elevator falls to the bottom of the shaft.

2) If the maximum tension for the cable is exceeded, then the cable snaps and the elevator falls to the bottom of the shaft.

3) If we raise and lower the elevator by letting out or pulling in cable at a fixed velocity (say 2 ft/second - so it takes 4 seconds to go up one 8 ft floor and 40 seconds to go up 10 - 8 foot floors {89 ft}, what is the acceleration of the elevator for most of the journey (excluding the very start and the end of the trip)?

Remember: acceleration is the rate of change of velocity.

4) Would you get on an elevator that has a significant acceleration (other than for a joy ride?)

5) Do you know where the value of g comes from?

 

[haruspex]

What is OP?

OP can mean the Original Post (post #1 in the thread) or Original Poster (you, in this case).

 

[Viraam]

That is correct.

1) The tension in the cable can only go to 0. If we want the elevator to go down faster, we would have to attach a cable to the bottom of the elevator and pull it. With no tension, the elevator falls to the bottom of the shaft.

2) If the maximum tension for the cable is exceeded, then the cable snaps and the elevator falls to the bottom of the shaft.

3) If we raise and lower the elevator by letting out or pulling in cable at a fixed velocity (say 2 ft/second - so it takes 4 seconds to go up one 8 ft floor and 40 seconds to go up 10 - 8 foot floors {89 ft}, what is the acceleration of the elevator for most of the journey (excluding the very start and the end of the trip)?

Remember: acceleration is the rate of change of velocity.

4) Would you get on an elevator that has a significant acceleration (other than for a joy ride?)

5) Do you know where the value of g comes from?

3) Is the acceleration 0. When velocity is constant then acceleration is zero
$u = v \ \ \ \ \ \therefore a = \frac{v-v}{t}=0$
4) I didnt understand what you mean by significant acceleration? (do you mean appreciable acceleration)

 

[NickAtNight]

4) I didnt understand what you mean by significant acceleration? (do you mean appreciable acceleration)

Yes.

Lets go find an expert. From http://www.lift-report.de/index.php/news/176/368/Elevator-Ride-Quality "

Acceleration
Most people understand that acceleration is the rate of change of velocity. The effects of acceleration are both physical as well as psychological and will have major variances between people traveling in the elevator. Elevator acceleration is perceived as good when it is constant. If the acceleration is by noticeable steps it will be perceived as objectionable.
Obviously when slowing down an elevator will produce a negative acceleration curve which should mirror the step-less acceleration curve.
The passenger perception of acceleration is that for values below 1.1 m/s2 the majority of passengers would not have any perception of a difference in overall elevator ride quality. Acceleration and motion is noticeable if between 1.3 m/s2 and 1.6 m/s2, and in the majority of elevators this would be an optimum value for acceleration to provide a good quality of elevator ride comfort. Acceleration above 1.8 m/s2 would often be perceived as objectionable.

and earlier, here are some parameters they design to avoid: Noise, Quaking, Acceleration and Jerk:

From an analysis of four international elevator consultants ride comfort specifications for 1600 kg group of elevators at 4.0 m/sec in a common shaft the basic requirements were as detailed in table 1.
ISO 18 738 classifies noise, lateral quaking, acceleration and jerk as:

• Noise – Sound – a weighted sound pressure level in decibels.
• Lateral Quaking – A sideways acceleration measured in m-g.
• Acceleration – A rate of acceleration measured on the z-axis velocity and expressed in metres per second squared (m/s2).
• Jerk – The rate of change of z-axis acceleration, attribute to lift motion control and expressed in metres per second cubed (m/sec3).

 

[NickAtNight]

Here* they are designing between 2 to 5 ft/s^2

*APPLIED INDUSTRIAL CONTROL SOLUTIONS ApICS LLC. Elevator Modeling and DC Drive Speed Controller DesignBrian T. Boulter