CN Tower Elevator
Problem statement:
A model of the CN Tower is put on a scale in an elevator in the CN Tower. As the elevator descends the weight of the model at first decreases
and then returns to normal as the elevator continues down.
When the elevator comes to a stop the weight increases and then returns to normal.
From the observations of the apparent weight changes and the timings, estimate the change of elevation during the elevator descent.
- Mass of model: $m = $ 1.52 kg
- Apparent mass reading of model during start of descent: $ m_1 = 1.42$ kg.
- Duration of nonzero acceleration while starting descent and stopping descent: $t_s = $ 8 s, each.
- Duration of descent, start to stop (including periods of non-zero acceleration) : $t_d =63$ s
To find: What is the change of elevation of the elevator ride?
Solution
- What is the acceleration during start of descent?
$$a = \frac{F_{\rm net}}{m}= \frac{- mg + F_N}{m}$$
where
$$F_N = m_1 g$$
so
$$a = -g + \frac{m_1}{m}g$$
- What is the change in velocity while starting descent?
$$\Delta v = a t_s$$
Since it starts from rest, the velocity of descent is $v = \Delta v$.
- What is the distance covered during the period of constant $v$ while descending?
- What is the distance covered during the periods of constant acceleration while starting and stopping descent?
From left to right:
- Burj Khalifa, Dubai
- CN Tower, Toronto
- Willis Tower, Chicago (aka, Sears Tower)
N. Alberding, 2013