Calculating Power Needed for a Ski Tow at a Resort: Work & Power Question

[Speedking96]

Homework Statement

The ski tow at a ski resort takes 1000 people per hour to a height of 500 m. The average mass of the skiers using this tow is 60 kg. In the normal operation of the ski tow, the energy lost to fictional forces is 60%.

How much power is required to run the ski tow?

2. The attempt at a solution

Power = (work) / (time)

= (mgh) / (time)

= ( (60*1000) ( 9.81) (500) ) / (3600)

= 81750 Watts.

However, it will need an additional 60% of Power.

Thus: 81750 * 1.60 = 130,800 Watts.

 

[Doc Al]

However, it will need an additional 60% of Power.

Thus: 81750 * 1.60 = 130,800 Watts.

Careful. The energy lost to friction is 60% of the total provided. So what percentage of the total is 81750?

 

[BvU]

So, what's your question? Your attempt is quite sensible, only:
If I were to do this one, I would reason: the 82 kW is the 40% remaining, so the required power is 100/40*82 kW = 205 kW.
I don't think a ski resort at sea level is such a success, but perhaps they mean: to a height 500 meter above the resort...

 

[Speedking96]

Careful. The energy lost to friction is 60% of the total provided. So what percentage of the total is 81750?

Isn't it just the 60% of the energy required to reach 500 meters?

I don't understand why the 81750 Watts are only 40% of the required power.

 

[Doc Al]

Isn't it just the 60% of the energy required to reach 500 meters?

No. Friction is 60% of the total energy; The energy needed to raise the lift is thus 40% of the total. You have to find the total.

 

[Speedking96]

No. Friction is 60% of the total energy; The energy needed to raise the lift is thus 40% of the total. You have to find the total.

Ah. I see. Thank you.