A ski tow operates on a slope of angle 15.9 ? of length 320 m . The rope moves a

Question

A ski tow operates on a slope of angle 15.9? of length 320m . The rope moves at a speed of 11.9km/h and provides power for 48 riders at one time, with an average mass per rider of 72.0kg . Estimate the power required to operate the tow.
A ski tow operates on a slope of angle 15.9? of length 320m . The rope moves at a speed of 11.9km/h and provides power for 48 riders at one time, with an average mass per rider of 72.0kg . Estimate the power required to operate the tow.
A ski tow operates on a slope of angle 15.9? of length 320m . The rope moves at a speed of 11.9km/h and provides power for 48 riders at one time, with an average mass per rider of 72.0kg . Estimate the power required to operate the tow.
A ski tow operates on a slope of angle 15.9? of length 320m . The rope moves at a speed of 11.9km/h and provides power for 48 riders at one time, with an average mass per rider of 72.0kg . Estimate the power required to operate the tow.
A ski tow operates on a slope of angle 15.9? of length 320m . The rope moves at a speed of 11.9km/h and provides power for 48 riders at one time, with an average mass per rider of 72.0kg . Estimate the power required to operate the tow.
Estimate the power required to operate the tow.

Explanation / Answer

Angle = 15.9o

Speed of the rope = 11.9 km/h

Average mass per ride = 72.0 kg

Total mass per ride is, m = 48*72 = 3456 kg

First convert the speed to m/s:

     11.9 km/hr = 11900 m /3600 s = 3.3056 m/s

The rate of increase of PE of the riders is:

   P = ?U / t   = mg ?h / t    = m g d sin? / t   =   m g sin? (d/t) = m g v sin?

where i replaced "d/t", the rate at which the skiers movealong the incline, with v.

Now, power is P = 3456* 9.8 * 3.3056*sin15.9o = 30671.16 W or 30.67 kW

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