Calculate the horsepower of the motor of an elevator, which can carry $10$ persons of the average mass of $60 k g$ through a vertical height of $20 m$ in $30 s$ . [Take g = $10 N / k g$ , $1 H P = 750 W$ ]

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Solution

Step 1: Given data,
No. of persons= $10$
The average mass of one person=mass of one person= $60 k g$
Height= $20 m$
Time= $30 s$
Acceleration due to gravity g= $10 N / k g$
Step 2: To find the mass of $10$ persons:
Mass of one person= $60 k g$
Mass of $10$ persons= $10 \times 60 = 600 k g$
Step 3: To find force and work done
Formula used= $f o r c e = w e i g h t = m g$
F= $600 \times 10 = 6000 N$
Work done in terms of force and displacement is,
Formula used: $w o r k d o n e = f o r c e \times d i s p l a c e m e n t$
$W = 6000 \times 20 W = 120000 J$
Step 4: To find power,
Formula used: $p o w e r = \frac{w o r k}{t i m e}$
$P = \frac{120000}{30} = 4000 w a t t s$
Step 5: To convert watts into horsepower,
$1 H P = 750 W$ $1 W = \frac{1}{750} H P$
$4000 W = \frac{4000}{750} = 5.33 H P$
Thus, the value of power in the horsepower unit is $5.33 H P$ .

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