Gravitation potential energy question help

In summary, the problem involves a skier who weighs 68.5 kg riding a ski lift that is 2.56 km long and at an angle of 13.9° to the horizontal. The skier's gravitational potential energy at the top of the mountain relative to the base is determined using the equation Eg = mgy. After correcting for the angle, the correct answer is 4.13x10^5 J.
  • #1
jbjohnybaker
19
0

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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  • #2
hello,

you have not accounted for the angle. the ski lift does not go straight up, it goes up a slope.
 
  • #3
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
 
  • #4
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.
 
  • #5
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)
 
  • #6
looks good.
 
  • #7
thank you very much.
 
  • #8
cheers.
 

1. What is gravitational potential energy?

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It is the potential of an object to do work as a result of its vertical position or height.

2. How is gravitational potential energy calculated?

The calculation for gravitational potential energy is mass multiplied by the acceleration due to gravity (9.8 m/s2) multiplied by the vertical height of the object.

3. What factors affect gravitational potential energy?

The factors that affect gravitational potential energy include the mass of the object, the acceleration due to gravity, and the vertical height of the object.

4. What is the relationship between gravitational potential energy and kinetic energy?

Gravitational potential energy and kinetic energy are both forms of mechanical energy. As an object falls, its gravitational potential energy decreases while its kinetic energy increases. This relationship allows for the conversion of potential energy into kinetic energy and vice versa.

5. How is gravitational potential energy used in real life?

Gravitational potential energy is used in various real-life applications, such as hydroelectric power plants where the potential energy of water stored in a dam is converted into kinetic energy to generate electricity. It is also used in roller coasters, where the potential energy of the cars at the top of a hill is converted into kinetic energy as they go down the track.

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