Question

HELP! A helicopter winches up an injured person from a boat. The person plus the equipment that must be pulled up with the person has a mass of 109 kg. The efficiency of the motor (the actual work done divided by the electrical energy consumed expressed as a percentage) is 69%. If the height of the lift is 83 m and it is carried out at a uniform rate over 55 s, what is the power expended by the helicopter's winch motor? (Give your answer in Watts)

Answer 1

When a person is pulled upwards why the motor of the helicopter

Then the potential energy increased  of the person is given as

$U = mgh$

here m = 109 kg

h = 83 m

so here potential energy of the person given as

$U = 109*9.8*83$

$U = 88660.6 J$

now power is defined as rate of energy

so it took 55 s to pull the mass so power is given as

$P = \frac{U}{t} = \frac{88660.6}{55} = 1612 W$

now we know that efficiency of motor is given as 69%

so we have

$efficiency = \frac{output}{input}$

$0.69 = \frac{1612}{P}$

so we have power as

$P = \frac{1612}{0.69} = 2336.2 W$