Question

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

Short answer

The average power required of the force making the lift is$1.65\times {10}^5\mathrm{W}$

Step-by-step solution

Given information

It is given that,

1. Weight of the passenger is W=660kg
2. The height through which the lift is raised is d=150m
3. The time taken by the lift to raise is 60.0s .
4. The speed of the lift is constant.

Determining the concept

The problem is based on Newton’s second law of motion which states that the rate of change of momentum of a body is equal in both magnitude and direction of the force acting on it.Find the velocity of the lift from its displacement and time. Then applying Newton’s second law, find the net force acting on it. From these two values, find the average power required of the force making the lift, using the corresponding formula.

Formulae:

$$\begin{gathered} P=Fv \\ {F}_{net}=0 \end{gathered}$$

Where,

$F_{net}$Is net force,v is velocity and Pis the power.

Determining the average power required of the force making the lift

The velocity of the lift is,

$$\begin{gathered} v=\frac{150}{60} \\ v=2.5\mathrm{m}/\mathrm{s} \end{gathered}$$

The speed of the lift is constant, its acceleration is zero, and net force acting on it is weight of passengers.

$F=100\mathrm{W}$

$=100\left(660\right)$

$F=6.6\times {10}^4\mathrm{N}$

Now,

$$\begin{gathered} P=Fv \\ P=6.6\times {10}^4\left(2.5\right) \\ =1.65\times {10}^5\mathrm{W} \end{gathered}$$

Therefore, the average power required of the force making the lift is$1.65\times {10}^5\mathrm{W}$.