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

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Homework Help Overview

The discussion revolves around calculating the gravitational potential energy of a skier on a ski lift, specifically addressing the skier's mass, the lift's angle, and the distance traveled along the lift.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the importance of accounting for the angle of the ski lift in determining the vertical displacement (delta y) for the potential energy calculation. There is a focus on clarifying the distinction between the total distance traveled and the actual change in altitude.

Discussion Status

Participants are actively engaging in clarifying the correct approach to calculating gravitational potential energy, with some suggesting corrections to the initial calculations based on the angle of the lift. There is a recognition of the need to accurately determine delta y.

Contextual Notes

There is an emphasis on the distinction between the length of the ski lift and the vertical height gained, which is critical for the potential energy calculation. Some participants express confusion regarding the definitions and values used in the calculations.

jbjohnybaker
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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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