How Does a Skier's Energy Change Through Different Stages?

In summary, the signs of energy in each stage of the scenario are Positive, Positive, Positive, and Negative. Stage 1 is positive because the work done is in the same direction as the displacement. Stage 2 is positive because the skier has a lot of potential energy at the top of the mountain. Stage 3 is positive because the skier has a lot of kinetic energy at the bottom of the mountain. Stage 4 is negative because the skier is being stopped by a force in the opposite direction of their displacement.
  • #1
katj
3
0
"A skier (total mass, ski included) catches a ride on a life to the top of a mountain (Stage 1 to stage 2). Once at the top, the skier heads down the slope, reaches the base of the mountain (Stage 3), and coasts to a stop (Stage 4).

Stage 1: Work done on the skier by the chairlift.
Stage 2: Potential Energy of the skier at the mountaintop.
Stage 3: Kinetic energy of the skier at the bottom of the mountain.
Stage 4: Work done on the skier to come to a stop.

Us this scenario to describe the signs (positive or negative) of the energy in each of these stages of the scenario.

A. Positive, Positive, Positive, Positive
B. Positive, Positive, Positive, and Negative
C. Positive, Positive, Negative, Positive
D. Negative, Positive, Positive, Negative
E. Negative, Positive, Positive, Positive

I am thinking that the answer should E, but I am not sure. It takes energy to do work, so stages 1 and 4 would be negative (I guess?). Stages 2 and 3 describe energy that the skier HAS, so they would be positive. I think!
 
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  • #2
katj said:
It takes energy to do work, so stages 1 and 4 would be negative (I guess?).
I don't understand your reasoning here. Hint: If the energy has increased, the work done was positive.
Stages 2 and 3 describe energy that the skier HAS, so they would be positive.
Makes sense.
 
  • #3
welcome to pf!

hi katj! welcome to pf! :smile:

work done is force times displacement (technically, force "dot" the displacement of the point of application of the force), so it'll be positive if the force is in the same direction as the displacement, and negative if it's in the opposite direction :wink:

and potential energy is defined as minus the work done (by a conservative force, such as gravity)

does that help? :smile:
 
  • #4
Let me try again! Does this make more sense?

Stage 1- positive because the force is in the same direction as displacement
Stage 2- positive because the skier would have lots of potential energy at the top
Stage 3- positive because the skier would have lots of kinetic energy at the bottom
Stage 4- negative because the displacement is forward and the force (of friction) is going back

PS- Thanks for the help!
 
  • #5
Good!
 
  • #6
Yay! Thanks for all of the help! This makes sense now!
 

Related to How Does a Skier's Energy Change Through Different Stages?

1. How does the change in energy of a skier affect their speed?

The change in energy of a skier directly affects their speed. According to the law of conservation of energy, the total energy of a system remains constant. As the skier gains or loses energy, their speed will increase or decrease accordingly.

2. Does the change in energy of a skier depend on their mass?

Yes, the change in energy of a skier does depend on their mass. Objects with larger mass require more energy to change their speed compared to objects with smaller mass. Therefore, a skier with a larger mass will experience a greater change in energy compared to a skier with a smaller mass.

3. Can a skier's change in energy be negative?

Yes, a skier's change in energy can be negative. This occurs when the skier loses energy, such as when they are slowing down or coming to a stop. Negative change in energy is also known as energy dissipation or energy loss.

4. How does the slope of the ski hill affect the change in energy of a skier?

The slope of the ski hill plays a significant role in the change of energy of a skier. A steeper slope will require the skier to use more energy to maintain their speed or accelerate, while a gentler slope will require less energy. This is due to the work-energy principle, which states that the amount of work done on an object is equal to the change in its kinetic energy.

5. Is the change in energy of a skier affected by external factors such as wind or friction?

Yes, external factors such as wind and friction can affect the change in energy of a skier. Wind resistance can slow down a skier, leading to a decrease in their energy. Friction from the snow or their equipment can also affect their energy, as it requires additional work to overcome. These external factors can impact the skier's overall performance and speed on the slopes.

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