# Elevator Free Fall: Calculating Energy & Spring Constant

• electriceel
In summary: X ^2K = 100,000/X^2K = 100,000/1^2K = 100,000In summary, an elevator car weighing 50,000 N is 27m from the ground. The cable snaps and the elevator goes into free fall. Shock absorbers have been provided and the coil length is 1 m. The total energy of the elevator at the bottom of the shaft, taking into account work done by friction, is 1,290,000. Using the work energy principle, the spring constant is determined to be 100,000.
electriceel
an elevator car weighing 50,000 N is 27m from the ground. the cable snaps and the elevator goes into free fall. Shock absorbers have been provided, the coil length is 1 m.

Assume elevator is able to lock onto the shaft at the point of contact w/ the absorber so that it does not bounce back. When elevator comes into contact w/ absorbers there is friction force of 60,000N acting on it as it descends that 1 m distance.

(A) Total energy of the elevator 27m above ground?
MGH= 50,000N*27
MGH = 1,350,000

(B)At the bottom of the shaft,when elevator comes to rest what is the total energy (take into account work done by friction)

MGH= 0 KE = 1/2 M V2- Friction

1/2 5000 V2=1,350,000-60,000
V2=564
V=24

Total energy: 1290000 ?

(C)Use work energy principal to determine spring constant K.

MGH= 50,000N* -1 = -50,000N
SPE = 1/2Kx2 = 1/2 K

-50,000+1/2 K = 1,290,000

K= 2,680,000

This doesn't seem correct.

it looks very good (and a well posted question and attempt at solution!) up until part c:

The energy stored in a spring is 1/2kX^2

Equate this to the energy lost by "friction",

Thank you Denverdoc.

Is this what you mean?

MGH= 50,000N* -1 = -50,000N
SPE = 1/2Kx2 = 1/2 K (1)

-50,000 + 1/2 K (1) = 60,000 N (??)

1/2 K = 110,000

K= 220,000

not quite: mgh = 1/2 kx^2. The kneticenergy gets converted to the potemtial energy of the spring.

Is this what you mean?

50,000 = 1/2 K X ^2

100,000 = K

## 1. What is an elevator free fall?

An elevator free fall occurs when an elevator is falling without any external forces acting on it, such as gravity or air resistance. This means that the elevator is accelerating towards the ground at a constant rate.

## 2. How is energy involved in elevator free fall?

In an elevator free fall, energy is being converted between potential energy and kinetic energy. As the elevator falls, its potential energy decreases while its kinetic energy increases. At the bottom of the fall, all of the potential energy is converted into kinetic energy.

## 3. How is the spring constant related to elevator free fall?

The spring constant is a measure of the stiffness of a spring. In the context of elevator free fall, the spring constant is used to calculate the force exerted by the spring when the elevator reaches the bottom of its fall. This force determines how quickly the elevator will come to a stop.

## 4. Can the energy of an elevator free fall be calculated?

Yes, the energy of an elevator free fall can be calculated using the formula E = mgh, where E is energy, m is the mass of the elevator, g is the acceleration due to gravity, and h is the height of the elevator's fall. This calculation assumes that all of the energy is being converted between potential and kinetic energy with no losses to friction or air resistance.

## 5. Are there any safety concerns with elevator free fall?

Elevator free fall is a controlled and planned process that is used in some amusement park rides, but it is not typically used in elevators for safety reasons. Without proper safety measures, elevator free fall can be dangerous and potentially cause injuries to passengers. Elevators are designed to use braking systems to control their descent and prevent free fall.

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