What Is the Maximum Acceleration a Cross-Country Skier Can Achieve Uphill?

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SUMMARY

The maximum acceleration a cross-country skier can achieve uphill on a 5º slope, using only her skis for propulsion, is calculated to be 1.4 m/s². This value is derived from the net force equation Fnet = ma, factoring in the static and kinetic friction coefficients (μs = 0.12, μk = 0.07) and the gravitational force component acting on the skier. The calculation involves the cosine of the angle of the slope and the acceleration due to gravity, confirming the skier's weight component must be considered in the overall force analysis.

PREREQUISITES
  • Understanding of Newton's second law (Fnet = ma)
  • Knowledge of static and kinetic friction coefficients
  • Basic trigonometry, particularly cosine functions
  • Familiarity with gravitational force calculations
NEXT STEPS
  • Study the effects of different slope angles on acceleration in physics
  • Explore advanced friction models in sports physics
  • Investigate the role of ski design in propulsion and acceleration
  • Learn about the impact of body weight on performance in uphill skiing
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Physics students, sports scientists, and coaches interested in optimizing cross-country skiing techniques and understanding the mechanics of uphill acceleration.

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Homework Statement



cross-country skier is going up a slope at angle 5º to the horizontal. She is skating so only her skis provide the propulsion (i.e. she does not push with her ski poles). The static and kinetic friction coefficients for this situation are μs = 0.12, μk = 0.07 respectively.

what is the maximum accelleration she can obtain?

Homework Equations



Fnet=ma

The Attempt at a Solution



so far i have got to (0.17-0.02)*9.8 *cos85=a

which equates to 1.4m/s^2 is this correct?

I got it by dividing the 9.8*cos85 and the mass (which canceled out).

Juswanted to know if its right as i don't have the answer and been working on it for a while.
 
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What about her weight component (the gravity force)?
 

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