Physics Problem Conservation of Energy

In summary, a skier with a mass of 60.0 kg starts from rest at the top of a 60.0 m high ski slope and descends with a speed of 28.8 m/s at the bottom. Moving horizontally, the skier crosses a patch of soft snow and reaches a speed of 6.35 m/s. The skier then hits a snowdrift and penetrates 2.9 m into it before coming to a stop. The average force exerted on the skier by the snowdrift cannot be calculated using the given information.
  • #1
John_Smithson
2
0

Homework Statement


A 60.0 kg skier starts from rest at the top of a ski slope 60.0 m high.

Homework Equations





The Attempt at a Solution


(a) If frictional forces do -10.5 kJ of work on her as she descends, how fast is she going at the bottom of the slope?
This one I got correct, it's 28.8 m/s.

(b)Now moving horizontally, the skier crosses a patch of soft snow, where µk = 0.2. If the patch is 85.0 m wide and the average force of air resistance on the skier is 160 N, how fast is she going after crossing the patch?
This one I also have correct, 6.35 m/s

(c) The skier hits a snowdrift and penetrates 2.9 m into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?

I derived the equation F = m*(Velocity from answer B)^2/(2*2.9m). This gets me 417N. However, it is not the right answer. I also know that the sign is not the problem, as neither 417N or -417N give the right answer. I used the work energy theorem to get F*d = 1/2m(VB)^2, and then just divided the kinetic energy by the distance to get the average Force. I don't know what I am doing worng.
 
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  • #2
I get 417 N, too.

If the deceleration is not uniform and the force gets averaged over time, the value can be different (and you cannot calculate it with additional information), but that cannot be the issue here.
 
  • #3
If I do the calculations using g = 9.807 m/s the result is 414 N. I wonder how sensitive the marking bot is to sig figs here?
 
  • #4
Even though the highest sig figs in the problem is 3, it does expect you to use g = 9.807 instead, and 414N was correct. Thanks.
 
  • #5
Part c is a wrong question. This comes up regularly. You cannot compute the "average force" from the energy and the distance. Yes, you can compute an average over distance, but consider this: average acceleration is defined as an average over time, Δv/Δt. So the reasonable definition of average force is also over time; for constant mass it's mΔv/Δt. That is not in general the same as an average ov distance.
 

What is conservation of energy?

Conservation of energy is a fundamental principle in physics which states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

How is conservation of energy applied in physics problems?

Conservation of energy is applied in physics problems by using it as a tool to analyze and solve problems related to the transfer and conversion of energy. It allows us to determine the initial and final energy states of a system and how energy is conserved throughout the process.

What are the different forms of energy that are conserved?

The different forms of energy that are conserved include kinetic energy, potential energy, thermal energy, electrical energy, and nuclear energy. These forms of energy can be converted into one another, but the total energy of a closed system remains constant.

Can energy be lost in a closed system?

No, energy cannot be lost in a closed system according to the law of conservation of energy. This means that the total energy of a closed system remains constant and any changes in energy are due to transfers or conversions between different forms of energy.

How is conservation of energy related to the first law of thermodynamics?

The law of conservation of energy is essentially the first law of thermodynamics, which states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. This principle is the basis for understanding how energy behaves in different systems and processes.

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