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

[jbjohnybaker]

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

 

[eczeno]

hello,

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

 

[jbjohnybaker]

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

 

[eczeno]

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.

 

[jbjohnybaker]

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)

 

[eczeno]

looks good.

 

[jbjohnybaker]

thank you very much.

 

[eczeno]

cheers.