How Is Gravitational Potential Energy Calculated for a Skier on a Ski Lift?

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SUMMARY

The gravitational potential energy (Eg) of a 68.5-kg skier at the top of a 2.56-km ski lift inclined at 13.9° is calculated using the formula Eg = mg delta y. The correct vertical displacement (delta y) must account for the angle of the lift, which was initially overlooked. The accurate calculation is Eg = (68.5)(9.81)(2560)(sin(13.9°)), resulting in a potential energy of approximately 4.13 x 10^5 J, aligning with textbook values.

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Homework Statement



A 68.5-kg skier rides a 2.56-km ski lift from the base of a mountain to the top. The lift is at an angle of 13.9° to the horizontal. Determine the skier’s gravitational potential energy at the top of the mountain relative to the base of the mountain.

Homework Equations


Eg= mg delta y

The Attempt at a Solution



eg = (68.5)(9.81)(2560)
= 1720281.6 J

The answer in the textbook is 4.13x10^5 J :S
 
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hello,

you have not accounted for the angle. the ski lift does not go straight up, it goes up a slope.
 
eczeno said:
hello,

you have not accounted for the angle. the ski lift does not go straight up, it goes up a slope.

I have been taught that "the value of delta y is the vertical displacement of the object. This means that the horizontal path of an object follows in changing its vertical height is not significant" :S
 
that is correct, but you have the wrong value for delta y. the lift travels a total distance of 2.56 km, but that is not the change in altitude, that is how long the cables are.
 
eczeno said:
that is correct, but you have the wrong value for delta y. the lift travels a total distance of 2.56 km, but that is not the change in altitude, that is how long the cables are.

is it right?

eg = (68.5)(sin13.5)(9.81)(2560)
 
looks good.
 
thank you very much.
 
cheers.
 

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