An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being <math> <mn>68</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </math> . The mass of the elevator itself is <math> <mn>920</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </math> and it moves with a constant speed of <math> <mn>3</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </math> . the frictional force opposing the motion is <math> <mn>6000</mn> <mtext> </mtext> <mi mathvariant="normal">N</mi> </math> . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator <math> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">g</mi> <mo>=</mo> <mn>10</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>/</mo> <msup> <mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfenced> </math> must be at least:

Net force on motor will be F min = [ 920 + 68 ( 10 ) ] g + 6000 <!- [endif]-><!- [endif]-> = 22000 N <!- [endif]-><!- [endif]->So, required power for motor P min = F ? min ⋅ v ? = 22000 × 3 = 66000 watt <!- [endif]-><!- [endif]->

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being <math> <mn>68</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </math> . The mass of the elevator itself is <math> <mn>920</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </math> and it moves with a constant speed of <math> <mn>3</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </math> . the frictional force opposing the motion is <math> <mn>6000</mn> <mtext> </mtext> <mi mathvariant="normal">N</mi> </math> . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator <math> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">g</mi> <mo>=</mo> <mn>10</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>/</mo> <msup> <mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfenced> </math> &nbsp;must be at least: &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics Class 11th Work, Energy and Power

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68 k g$ . The mass of the elevator itself is $920 k g$ and it moves with a constant speed of $3 m / s$ . the frictional force opposing the motion is $6000 N$ . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $(g = 10 m / s^{2})$ must be at least:

Option 1 -

$56300 W$

Option 2 -

$66000 W$

Option 3 -

$62360 W$

Option 4 -

$48000 W$

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

Net force on motor will be

$F_{min} = [920 + 68 (10)] g + 6000$

$= 22000 N$

So, required power for motor

$\begin{array}{r} P_{min} & = {\overset{?}{F}}_{min} \cdot \overset{?}{v} \\ = 22000 \times 3 \\ = 66000 watt \end{array}$

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