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An elevator (mass 4850 kg) is to be designed so that themaximum acceleration is 0.0600g. What is the maximum and the minimum forces the motor should e

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asked 2021-04-26
An elevator (mass 4850 kg) is to be designed so that themaximum acceleration is 0.0600g. What is the maximum and the minimum forces the motor should exert on the supportingcable?
I already know how to find the maximum force (just multiplyingthe maximum acceleration by the mass), but I've got no clue as tohow to find the minimum acceleration when no minimum accelerationhas been found.

Expert Answers (1)

2021-04-28
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In both cases the free body diagram is as shown
Chossing the upward direction as positive,the Maximun tension is obtained by assuming the upward accelerationas positive.
Therefore, \(\displaystyle\triangle{F}={m}{a}\)
\(\displaystyle{F}_{{t}}-{m}{g}={m}{a}\)
Or \(\displaystyle{F}_{{t}}={m}{\left({a}+{g}\right)}\)
\(\displaystyle={m}{\left({0.0600}{g}+{g}\right)}\)
The minimum acceleration is obtained by assuming theacceleration is down.
Therefore, here \(\displaystyle{F}_{{t}}={m}{\left(-{a}+{g}\right)}\)
\(\displaystyle={m}{\left(-{0.0600}{g}+{g}\right)}\)
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