Skier down a slope and potential energy

In summary, the problem is asking for the percentage of energy lost by a woman skiing down a 100 m slope with a speed of 20 m/s at the bottom. This can be calculated by finding the difference between her potential energy at the top and kinetic energy at the bottom, and then dividing that by her potential energy at the top. This is equivalent to the formula 1 - (KE2/PE2). It is also important to note that the one in the formula represents the initial energy, and the fraction represents the energy lost. The result will be the same regardless of which formula is used.
  • #1
rkslperez04
31
0
Here is the question:

A women skis down a slope 100 m high. Her speed at the foot of the slope is 20 m/s. What percentage of her intial potential engery is lost?


okkk.. here is what I get:

My instructor mentioned this was a Ef/Ei problem. (effientcy final divided by effientcy intial)

my book uses the formula: 1 - (KE2/PE2)

Im confused where the one came from?

then...

I understand we have PE at the top of the hill only being we are to assume she is at rest... so no KE. So does that mean we no PE at the bottom only KE...


Im confused.. can someone explain this to me in laymens terms so I can rework the problem. Is there an easier way to solve this.??
 
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  • #2
rkslperez04 said:
Here is the question:

A women skis down a slope 100 m high. Her speed at the foot of the slope is 20 m/s. What percentage of her intial potential engery is lost?


okkk.. here is what I get:

My instructor mentioned this was a Ef/Ei problem. (effientcy final divided by effientcy intial)

my book uses the formula: 1 - (KE2/PE2)

Im confused where the one came from?

then...

I understand we have PE at the top of the hill only being we are to assume she is at rest... so no KE. So does that mean we no PE at the bottom only KE...


Im confused.. can someone explain this to me in laymens terms so I can rework the problem. Is there an easier way to solve this.??
Yes, you are on the right track. She has only PE at the top. At the bottom, no PE, just KE. Calculate her PE at the top. Calculate her KE at the bottom. How much energy was lost (due to friction, snow resistance, air resistance, etc.)? What percentage is that of the initial energy? The result is the same as (1 - E_f/E_i), where E_f and E_i are the final and initial energy, respectively. I don't understand either where the book formula came from.
 
  • #3
The amount of energy that was lost is

[tex]PE_t - KE_b[/tex]

where t refers to top and b to bottom. The fraction of energy lost will be

[tex]\frac{PE_t - KE_b}{PE_t}[/tex]

which comes to

[tex]1 - \frac{KE_b}{PE_t}[/tex]

the percentage will just be this fraction times one hundred.
 

1. What is potential energy in relation to a skier going down a slope?

Potential energy is the energy stored in an object due to its position or state. In the case of a skier going down a slope, potential energy is the stored energy that the skier has due to their height above the ground.

2. How does the skier's potential energy change as they go down the slope?

As the skier goes down the slope, their potential energy decreases. This is because as they move closer to the ground, their height decreases and therefore their potential energy decreases as well. This energy is then converted into kinetic energy as the skier gains speed.

3. What factors affect a skier's potential energy while going down a slope?

The factors that affect a skier's potential energy while going down a slope include their mass, the height of the slope, and the acceleration due to gravity. A heavier skier will have more potential energy, a steeper slope will have more potential energy, and a higher acceleration due to gravity will also increase potential energy.

4. How can potential energy be transformed into kinetic energy for a skier?

As the skier goes down the slope and their potential energy decreases, it is converted into kinetic energy. This is due to the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In this case, the potential energy is transformed into kinetic energy as the skier gains speed.

5. How does a skier's potential energy affect their speed while going down a slope?

A skier's potential energy directly affects their speed while going down a slope. As the skier's potential energy decreases, their speed increases. This is because the potential energy is converted into kinetic energy, which is the energy of motion. The more potential energy the skier has at the top of the slope, the faster they will go as they convert it into kinetic energy while going down the slope.

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