Question

If ski lift raises 100 passengers averaging 660 N in weight, a machine raises passengers averaging 667 N in weight to a height of 150 m in 60.0 s, at constant speed what aveage power is required of the force making the lift

Answer 1

Hi,

Hope you are doing well.

First of all let's find out the total mass in the lift which is given by,

11 = 100 × aug

Where,

aug
is the average force per person (N).

is the acceleration due to gravity (m/s²).

Given that,

Average force per person, $F_{avg}=667\;N$

Acceleration due to gravity, $g=9.8\;m/s^{2}$

$\therefore$ Total mass in the lift is given by,

$M=100\times\frac{F_{avg}}{g}=100\times\frac{667\;N}{9.8\;m/s^{2}}$

$\mathbf{\therefore M=6806.1224499\;kg}$

We know that, When the lift reaches a particular height, it will gain a potential energy which is given by,

$U=Mgh$

Where,

is the Total mass in the lift (kg).

is the acceleration due to gravity (m/s²).

is the height reached by the lift (m).

Given that,

Total mass in the lift, $M=6806.1224499\;kg$

Acceleration due to gravity, $g=9.8\;m/s^{2}$

Height reached by the lift, $h=150\;m$

$\therefore$ Potential energy gained by the lift is given by,

$U=Mgh=6806.1224499\;kg\times9.8\;m/s^{2}\times150\;m$

$\mathbf{\therefore U=10,005,000\;J}$

We know that, according to work energy theorem, the work done by the lift to lift is converted to potential energy.

$\therefore$ Work done by the lift is given by,

$W=U=10,005,000\;J$

We know that, Power required by the lift is given by,

$P=W\times t$

Where,

is the time taken (s).

Given that,

Time consumed for the lifting, $t=60.0\;s$

$\therefore$ Power required by the lift is given by,

$P=W\times t=10,005,000\;J\times 60.0\;s$

$\mathbf{\therefore P=600.3\;MW}$

$\left (\because 10^{6}\;W=1\;MW \right )$

Hope this helped for your studies. Keep learning. Have a good day.

Feel free to clear any doubts at the comment section.

Please don't forget to give a thumbs up.

Thank you. :)