Question

a crane is used to lift 10000kg of coal from mine 100metre deep .calculate the workdone, the time taken by the crane is one hour . calculate the power of the crane assuming the efficiency of the crane is 80%

Answer 1

Given :-

Mass m of the crane = 10000 kg

Displacement s = 100 m

To Find :-

Power of the crane  = ?

SoluTion :-

$\boxed {\sf {Work\ done = F \times s}}\\\\\\\\\sf {Work\ done =10000 \times 9.8 \times 100}\\\\\\\sf { = 98 \times 10^{5}\ joule}\\\\\\\\\sf {Power=\frac{w}{t} }\\\\\\\sf {Power = \frac{98 \times 10^{5}}{3600} }\\\\\\\sf {=2.722 \times 10^{3} \ watt }\\\\\\\\\sf {Efficiency = \frac{Power\ used\ to\ lift\ load}{Total \ Power} \times 100 }\\\\\\\sf {P=\frac{2.722 \times10^{3}}{80}\times 100=3403 \ watts }$

∴ Power of the crane = 3403 watts.

Answer 2

★★Question:-

✓✓A crane is used to lift 10000kg of coal from mine 100metre deep .calculate the workdone, the time taken by the crane is one hour . calculate the power of the crane assuming the efficiency of the crane is 80%.

★★Given :-

• Mass of the crane $(m)=10000kg$

• Displacement $(s)=100m$

• Taking $g\:=9.8m/{s}^{2}$

★★Explanation:-

Work done$=F×s$

$=(10000×9.8)×100$

$=98×{10}^{5}\:joule$

• We also know that power is work done in the given time or,

Power$=\dfrac{w}{t}$

$=\dfrac{98×10^5}{3600}$

$=2.722×{10}^{3}\:watt$

Now,

Efficiency

$=\dfrac{Power\:used\:to\:lift\:load}{Total\:power}×100$

$⇒P=\dfrac{2.722×10^3}{80}×100$

$=3403\:watts$✔️✔️

hence, we have power of the crane (P) to be 3403 watts.