Question

A ski tow operates on a slope of angle 14.0^\circ of length 250 m. The rope moves at a speed of 13.0 km/h and provides power for 54 riders at one time, with an average mass per rider of 75.0 kg.
Estimate the power required to operate the tow. ?

Answer 1

Answer:

The power required to operate the tow is 34.75 kW.

Explanation:

Given that,

A ski tow operates on a slope of angle, $\theta=14^{\circ}$

Speed of the rope, v = 13 km/h = 3.62 m/s

Number of riders, n = 54

The average mass per rider of 75.0 kg

We need to find the power required to operate the tow. We know that the rate at which the work is done is called power operated by an object.

$P=\dfrac{W}{t}\\\\or\\\\P=F\times v$

Here,

$P=54mg\times v\sin\theta\\\\P=54\times 75\times 9.8\times 3.62\times \sin(14)\\\\P=34758.8\ W$

or

P = 34.75 kW

So, the power required to operate the tow is 34.75 kW. Hence, this is the required solution.