In comparing traditional low-speed chairlifts with high-speed chairlifts, assumptions have been made (efficiency) by the two...

In comparing traditional low-speed chairlifts with high-speed chairlifts, assumptions have been made (efficiency) by the two chairlifts is the same if they travel same distance.

a) Does high-speed chairlift experience more frictoon than low speed chairlift due to air resistance and friction?

b) Could you please explain why this assumption is false?

Thank you so much!!

Expert Solution

I suppose the assumption is: "The efficiencies of low-speed chairlifts and high-speed chairlifts are the same if they travel same distance".

a) The ball bearing friction decreases with increase in speed and the drag force on the chairs due to air resistance increases with increase in speed. The effect of drag force is much larger than the ball bearing friction. In fact, the drag force is directly proportional to the square of the speed and to the cross sectional area of the chairs. The formula for the drag force due to air resistance is given by:

where, F_D is the drag force, is the density of the air, v is the speed of the obect relative to air, C_D is the drag coefficient and A is the cross-sectional area of the object.

Therefore, high speed chairlift experiances more friction than low speed chairlift.

b) As the high speed chairlift experiances more friction than low speed chairlift, more energy needs to be consumed to operate high speed chairlift. Therefore, high speed chairlift is less energy efficient than low speed chairlift. Therefore the assumption is false.

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genius_generous answered 2 years ago

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