A loaded elevator with very worn cables has a total mass of 2200 kg, and the cables can withsta

(a) The free-body force diagram for the elevator would include two forces: the force of gravity

A loaded elevator with very worn cables has a total mass of...

A loaded elevator with very worn cables has a total mass of $2200 \mathrm{~kg},$ and the cables can withstand a maximum tension of $28,000 \mathrm{~N}$ (a) Draw the free-body force diagram for the elevator. In terms of the forces on your diagram, what is the net force on the elevator? Apply Newton's second law to the elevator and find the maximum upward acceleration for the elevator if the cables are not to break. (b) What would be the answer to part (a) if the elevator were on the moon, where $g=1.62 \mathrm{~m} / \mathrm{s}^{2} ?$

Transcript

00:02 Limit equal to 28 ,000 newtons and then the fully loaded mass of the elevator's cabin is 2 ,200 kilograms.

00:22 Then we have the gravitational acceleration on earth equal to 9 .81 meters per second squared.

00:35 Then the gravitational acceleration on the moon, which is 1 .62 meters per second squared.

00:48 So the first step is to write a force summation describing the elevator's vertical acceleration and its weight, which can be simplified as m times the quantity of a plus g.

01:12 So we can equate the tension limit at the elevator's cable to represent sigma f.

01:23 And then we have the mass of the elevator's cabin, 2 ,200 kilograms, times the quantity of a, which we do not know.

01:33 That is the maximum vertical acceleration limit, plus the gravitational acceleration on earth, which we do know.

01:41 So when we saw for a, we then compute 28 ,000 is equal to 2200 a plus 2200 times 9 .81.

01:58 This will equate the elevator's horse weight on earth, 21 ,582.

02:11 So then we then subtract the elevators horse weight on earth, 21 ,50082 from 28, and equal that to 2200a.

02:24 So upon solving for a, we get 6418 is equal to 2200a, where a is equal to 6418 divided into 2200, which is equal to 2 .92 meters per second squared, which is the maximum vertical acceleration the elevator can handle when on earth.

03:05 So if we apply a force summation regarding the elevator when on the moon, we then get the following.

03:19 Now the materials tension limit of the cable will not change regardless to the gravitational acceleration.

03:25 So again, wherever the elevator is, whether on the earth or the moon, the force tension limit will always equal $28 ,000.

03:39 So then we equate that to the mass, which will also not change regardless to gravitational acceleration, 2 ,200 kilograms times the acceleration, which we don't know, plus the gravitational acceleration on the moon, which we do know.

04:01 So when we work this out, we get 28 ,000 is equal to 2 ,200a plus 2 ,200 times.

04:14 1 .62 is 3564.

04:19 This is the force weight and mutants of the elevator when on the moon.

04:25 So when we saw for a, 3564 minus 28 ,000 is 24 ,4, 436 is equal to 2200a, and then a is equal to 24 ,000 -436.

04:49 Divided into 2 ,200, which is equal to 24 ,436 divided into 2 ,200 is equal to 11 .1 meters per second squared...

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